id	sid	tid	token	lemma	pos
ejpam-6178	1	1	european	european	PROPN
ejpam-6178	1	2	journal	journal	PROPN
ejpam-6178	1	3	of	of	ADP
ejpam-6178	1	4	pure	pure	ADJ
ejpam-6178	1	5	and	and	CCONJ
ejpam-6178	1	6	applied	applied	ADJ
ejpam-6178	1	7	mathematics	mathematic	NOUN
ejpam-6178	1	8	2025	2025	NUM
ejpam-6178	1	9	,	,	PUNCT
ejpam-6178	1	10	vol	vol	NOUN
ejpam-6178	1	11	.	.	PROPN
ejpam-6178	1	12	18	18	NUM
ejpam-6178	1	13	,	,	PUNCT
ejpam-6178	1	14	issue	issue	NOUN
ejpam-6178	1	15	4	4	NUM
ejpam-6178	1	16	,	,	PUNCT
ejpam-6178	1	17	article	article	NOUN
ejpam-6178	1	18	number	number	NOUN
ejpam-6178	1	19	6178	6178	NUM
ejpam-6178	1	20	issn	issn	VERB
ejpam-6178	1	21	1307	1307	NUM
ejpam-6178	1	22	-	-	SYM
ejpam-6178	1	23	5543	5543	NUM
ejpam-6178	1	24	–	–	PUNCT
ejpam-6178	1	25	ejpam.com	ejpam.com	X
ejpam-6178	1	26	published	publish	VERB
ejpam-6178	1	27	by	by	ADP
ejpam-6178	1	28	new	new	PROPN
ejpam-6178	1	29	york	york	PROPN
ejpam-6178	1	30	business	business	PROPN
ejpam-6178	1	31	global	global	PROPN
ejpam-6178	1	32	topological	topological	PROPN
ejpam-6178	1	33	homomorphisms	homomorphism	NOUN
ejpam-6178	1	34	in	in	ADP
ejpam-6178	1	35	a	a	DET
ejpam-6178	1	36	topological	topological	ADJ
ejpam-6178	1	37	dual	dual	ADJ
ejpam-6178	1	38	b	b	NOUN
ejpam-6178	1	39	-	-	PUNCT
ejpam-6178	1	40	algebra	algebra	VERB
ejpam-6178	1	41	rashin	rashin	PROPN
ejpam-6178	1	42	nuñez1,∗	nuñez1,∗	NOUN
ejpam-6178	1	43	,	,	PUNCT
ejpam-6178	1	44	katrina	katrina	PROPN
ejpam-6178	1	45	belleza	belleza	PROPN
ejpam-6178	1	46	fuentes1	fuentes1	PROPN
ejpam-6178	1	47	1	1	NUM
ejpam-6178	1	48	department	department	NOUN
ejpam-6178	1	49	of	of	ADP
ejpam-6178	1	50	computer	computer	NOUN
ejpam-6178	1	51	,	,	PUNCT
ejpam-6178	1	52	information	information	NOUN
ejpam-6178	1	53	sciences	science	NOUN
ejpam-6178	1	54	,	,	PUNCT
ejpam-6178	1	55	and	and	CCONJ
ejpam-6178	1	56	mathematics	mathematic	NOUN
ejpam-6178	1	57	,	,	PUNCT
ejpam-6178	1	58	school	school	NOUN
ejpam-6178	1	59	of	of	ADP
ejpam-6178	1	60	arts	art	NOUN
ejpam-6178	1	61	and	and	CCONJ
ejpam-6178	1	62	sciences	science	NOUN
ejpam-6178	1	63	,	,	PUNCT
ejpam-6178	1	64	university	university	NOUN
ejpam-6178	1	65	of	of	ADP
ejpam-6178	1	66	san	san	PROPN
ejpam-6178	1	67	carlos	carlos	PROPN
ejpam-6178	1	68	,	,	PUNCT
ejpam-6178	1	69	6000	6000	NUM
ejpam-6178	1	70	cebu	cebu	NOUN
ejpam-6178	1	71	city	city	NOUN
ejpam-6178	1	72	,	,	PUNCT
ejpam-6178	1	73	philippines	philippine	NOUN
ejpam-6178	1	74	abstract	abstract	ADJ
ejpam-6178	1	75	.	.	PUNCT
ejpam-6178	2	1	this	this	DET
ejpam-6178	2	2	paper	paper	NOUN
ejpam-6178	2	3	introduced	introduce	VERB
ejpam-6178	2	4	the	the	DET
ejpam-6178	2	5	topological	topological	ADJ
ejpam-6178	2	6	dual	dual	PROPN
ejpam-6178	2	7	b	b	NOUN
ejpam-6178	2	8	-	-	PUNCT
ejpam-6178	2	9	homomorphism	homomorphism	NOUN
ejpam-6178	2	10	in	in	ADP
ejpam-6178	2	11	a	a	DET
ejpam-6178	2	12	topological	topological	ADJ
ejpam-6178	2	13	dual	dual	ADJ
ejpam-6178	2	14	b	b	NOUN
ejpam-6178	2	15	-	-	PUNCT
ejpam-6178	2	16	algebras	algebras	PROPN
ejpam-6178	2	17	and	and	CCONJ
ejpam-6178	2	18	its	its	PRON
ejpam-6178	2	19	example	example	NOUN
ejpam-6178	2	20	.	.	PUNCT
ejpam-6178	3	1	moreover	moreover	ADV
ejpam-6178	3	2	,	,	PUNCT
ejpam-6178	3	3	this	this	DET
ejpam-6178	3	4	paper	paper	NOUN
ejpam-6178	3	5	also	also	ADV
ejpam-6178	3	6	presented	present	VERB
ejpam-6178	3	7	a	a	DET
ejpam-6178	3	8	python	python	NOUN
ejpam-6178	3	9	program	program	NOUN
ejpam-6178	3	10	to	to	PART
ejpam-6178	3	11	check	check	VERB
ejpam-6178	3	12	the	the	DET
ejpam-6178	3	13	homomorphism	homomorphism	NOUN
ejpam-6178	3	14	condition	condition	NOUN
ejpam-6178	3	15	of	of	ADP
ejpam-6178	3	16	the	the	DET
ejpam-6178	3	17	topological	topological	ADJ
ejpam-6178	3	18	dual	dual	PROPN
ejpam-6178	3	19	b	b	NOUN
ejpam-6178	3	20	-	-	PUNCT
ejpam-6178	3	21	homomoprphism	homomoprphism	NOUN
ejpam-6178	3	22	.	.	PUNCT
ejpam-6178	4	1	furthermore	furthermore	ADV
ejpam-6178	4	2	,	,	PUNCT
ejpam-6178	4	3	the	the	DET
ejpam-6178	4	4	topology	topology	NOUN
ejpam-6178	4	5	for	for	ADP
ejpam-6178	4	6	the	the	DET
ejpam-6178	4	7	quotient	quotient	NOUN
ejpam-6178	4	8	dual	dual	ADJ
ejpam-6178	4	9	b	b	X
ejpam-6178	4	10	-	-	PUNCT
ejpam-6178	4	11	algebra	algebra	NOUN
ejpam-6178	4	12	was	be	AUX
ejpam-6178	4	13	presented	present	VERB
ejpam-6178	4	14	using	use	VERB
ejpam-6178	4	15	the	the	DET
ejpam-6178	4	16	natural	natural	ADJ
ejpam-6178	4	17	dual	dual	ADJ
ejpam-6178	4	18	b	b	NOUN
ejpam-6178	4	19	-	-	PUNCT
ejpam-6178	4	20	homomorphism	homomorphism	NOUN
ejpam-6178	4	21	.	.	PUNCT
ejpam-6178	5	1	this	this	DET
ejpam-6178	5	2	quotient	quotient	NOUN
ejpam-6178	5	3	dual	dual	ADJ
ejpam-6178	5	4	b	b	PROPN
ejpam-6178	5	5	-	-	PUNCT
ejpam-6178	5	6	topological	topological	ADJ
ejpam-6178	5	7	space	space	NOUN
ejpam-6178	5	8	was	be	AUX
ejpam-6178	5	9	proven	prove	VERB
ejpam-6178	5	10	to	to	PART
ejpam-6178	5	11	be	be	AUX
ejpam-6178	5	12	a	a	DET
ejpam-6178	5	13	topological	topological	ADJ
ejpam-6178	5	14	dual	dual	ADJ
ejpam-6178	5	15	b	b	NOUN
ejpam-6178	5	16	-	-	PUNCT
ejpam-6178	5	17	algebra	algebra	NOUN
ejpam-6178	5	18	.	.	PUNCT
ejpam-6178	6	1	consequently	consequently	ADV
ejpam-6178	6	2	,	,	PUNCT
ejpam-6178	6	3	properties	property	NOUN
ejpam-6178	6	4	of	of	ADP
ejpam-6178	6	5	a	a	DET
ejpam-6178	6	6	topological	topological	ADJ
ejpam-6178	6	7	homomorphism	homomorphism	NOUN
ejpam-6178	6	8	were	be	AUX
ejpam-6178	6	9	determined	determine	VERB
ejpam-6178	6	10	.	.	PUNCT
ejpam-6178	7	1	the	the	DET
ejpam-6178	7	2	topological	topological	PROPN
ejpam-6178	7	3	dual	dual	PROPN
ejpam-6178	7	4	b	b	NOUN
ejpam-6178	7	5	-	-	PUNCT
ejpam-6178	7	6	isomorphism	isomorphism	NOUN
ejpam-6178	7	7	among	among	ADP
ejpam-6178	7	8	topological	topological	ADJ
ejpam-6178	7	9	dual	dual	PROPN
ejpam-6178	7	10	b	b	NOUN
ejpam-6178	7	11	-	-	PUNCT
ejpam-6178	7	12	algebras	algebras	PROPN
ejpam-6178	7	13	was	be	AUX
ejpam-6178	7	14	also	also	ADV
ejpam-6178	7	15	introduced	introduce	VERB
ejpam-6178	7	16	,	,	PUNCT
ejpam-6178	7	17	and	and	CCONJ
ejpam-6178	7	18	some	some	DET
ejpam-6178	7	19	results	result	NOUN
ejpam-6178	7	20	were	be	AUX
ejpam-6178	7	21	obtained	obtain	VERB
ejpam-6178	7	22	.	.	PUNCT
ejpam-6178	8	1	2020	2020	NUM
ejpam-6178	8	2	mathematics	mathematic	NOUN
ejpam-6178	8	3	subject	subject	NOUN
ejpam-6178	8	4	classifications	classification	NOUN
ejpam-6178	8	5	:	:	PUNCT
ejpam-6178	8	6	54a05	54a05	NUM
ejpam-6178	8	7	,	,	PUNCT
ejpam-6178	8	8	54c05	54c05	NUM
ejpam-6178	8	9	,	,	PUNCT
ejpam-6178	8	10	54c10	54c10	NUM
ejpam-6178	8	11	key	key	ADJ
ejpam-6178	8	12	words	word	NOUN
ejpam-6178	8	13	and	and	CCONJ
ejpam-6178	8	14	phrases	phrase	NOUN
ejpam-6178	8	15	:	:	PUNCT
ejpam-6178	8	16	topological	topological	ADJ
ejpam-6178	8	17	dual	dual	PROPN
ejpam-6178	8	18	b	b	NOUN
ejpam-6178	8	19	-	-	PUNCT
ejpam-6178	8	20	algebra	algebra	NOUN
ejpam-6178	8	21	,	,	PUNCT
ejpam-6178	8	22	quotient	quotient	VERB
ejpam-6178	8	23	dual	dual	ADJ
ejpam-6178	8	24	b	b	NOUN
ejpam-6178	8	25	-	-	PUNCT
ejpam-6178	8	26	topology	topology	NOUN
ejpam-6178	8	27	,	,	PUNCT
ejpam-6178	8	28	topological	topological	ADJ
ejpam-6178	8	29	dual	dual	PROPN
ejpam-6178	8	30	b	b	NOUN
ejpam-6178	8	31	-	-	PUNCT
ejpam-6178	8	32	homomorphism	homomorphism	NOUN
ejpam-6178	8	33	,	,	PUNCT
ejpam-6178	8	34	topological	topological	ADJ
ejpam-6178	8	35	dual	dual	PROPN
ejpam-6178	8	36	b	b	NOUN
ejpam-6178	8	37	-	-	PUNCT
ejpam-6178	8	38	isomorphism	isomorphism	ADJ
ejpam-6178	8	39	1	1	NUM
ejpam-6178	8	40	.	.	PUNCT
ejpam-6178	9	1	introduction	introduction	NOUN
ejpam-6178	9	2	over	over	ADP
ejpam-6178	9	3	the	the	DET
ejpam-6178	9	4	years	year	NOUN
ejpam-6178	9	5	,	,	PUNCT
ejpam-6178	9	6	the	the	DET
ejpam-6178	9	7	studies	study	NOUN
ejpam-6178	9	8	of	of	ADP
ejpam-6178	9	9	type	type	NOUN
ejpam-6178	9	10	(	(	PUNCT
ejpam-6178	9	11	2,0	2,0	NUM
ejpam-6178	9	12	)	)	PUNCT
ejpam-6178	9	13	algebras	algebra	NOUN
ejpam-6178	9	14	have	have	AUX
ejpam-6178	9	15	remained	remain	VERB
ejpam-6178	9	16	a	a	DET
ejpam-6178	9	17	rich	rich	ADJ
ejpam-6178	9	18	subject	subject	NOUN
ejpam-6178	9	19	of	of	ADP
ejpam-6178	9	20	exploration	exploration	NOUN
ejpam-6178	9	21	(	(	PUNCT
ejpam-6178	9	22	see	see	VERB
ejpam-6178	9	23	[	[	X
ejpam-6178	9	24	1	1	NUM
ejpam-6178	9	25	]	]	PUNCT
ejpam-6178	9	26	,	,	PUNCT
ejpam-6178	9	27	[	[	X
ejpam-6178	9	28	2	2	NUM
ejpam-6178	9	29	]	]	PUNCT
ejpam-6178	9	30	,	,	PUNCT
ejpam-6178	9	31	[	[	X
ejpam-6178	9	32	3	3	NUM
ejpam-6178	9	33	]	]	PUNCT
ejpam-6178	9	34	,	,	PUNCT
ejpam-6178	9	35	[	[	X
ejpam-6178	9	36	4	4	NUM
ejpam-6178	9	37	]	]	NUM
ejpam-6178	9	38	)	)	PUNCT
ejpam-6178	9	39	.	.	PUNCT
ejpam-6178	10	1	in	in	ADP
ejpam-6178	10	2	particular	particular	ADJ
ejpam-6178	10	3	,	,	PUNCT
ejpam-6178	10	4	j.	j.	PROPN
ejpam-6178	10	5	neggers	neggers	PROPN
ejpam-6178	10	6	and	and	CCONJ
ejpam-6178	10	7	h.s	h.s	PROPN
ejpam-6178	10	8	.	.	PROPN
ejpam-6178	10	9	kim	kim	PROPN
ejpam-6178	10	10	introduced	introduce	VERB
ejpam-6178	10	11	the	the	DET
ejpam-6178	10	12	b	b	NOUN
ejpam-6178	10	13	-	-	PUNCT
ejpam-6178	10	14	algebras	algebras	PROPN
ejpam-6178	10	15	and	and	CCONJ
ejpam-6178	10	16	its	its	PRON
ejpam-6178	10	17	characteristics	characteristic	NOUN
ejpam-6178	10	18	[	[	X
ejpam-6178	10	19	5	5	NUM
ejpam-6178	10	20	]	]	PUNCT
ejpam-6178	10	21	.	.	PUNCT
ejpam-6178	11	1	some	some	DET
ejpam-6178	11	2	subsequent	subsequent	ADJ
ejpam-6178	11	3	studies	study	NOUN
ejpam-6178	11	4	on	on	ADP
ejpam-6178	11	5	b	b	X
ejpam-6178	11	6	-	-	PUNCT
ejpam-6178	11	7	algebras	algebra	NOUN
ejpam-6178	11	8	have	have	AUX
ejpam-6178	11	9	drawn	draw	VERB
ejpam-6178	11	10	parallel	parallel	ADJ
ejpam-6178	11	11	results	result	NOUN
ejpam-6178	11	12	with	with	ADP
ejpam-6178	11	13	group	group	NOUN
ejpam-6178	11	14	theory	theory	NOUN
ejpam-6178	11	15	(	(	PUNCT
ejpam-6178	11	16	see	see	VERB
ejpam-6178	11	17	[	[	X
ejpam-6178	11	18	6	6	NUM
ejpam-6178	11	19	]	]	PUNCT
ejpam-6178	11	20	,	,	PUNCT
ejpam-6178	11	21	[	[	X
ejpam-6178	11	22	7	7	NUM
ejpam-6178	11	23	]	]	PUNCT
ejpam-6178	11	24	,	,	PUNCT
ejpam-6178	11	25	[	[	X
ejpam-6178	11	26	8	8	NUM
ejpam-6178	11	27	]	]	PUNCT
ejpam-6178	11	28	,	,	PUNCT
ejpam-6178	11	29	[	[	X
ejpam-6178	11	30	9	9	NUM
ejpam-6178	11	31	]	]	SYM
ejpam-6178	11	32	)	)	PUNCT
ejpam-6178	11	33	.	.	PUNCT
ejpam-6178	12	1	in	in	ADP
ejpam-6178	12	2	2022	2022	NUM
ejpam-6178	12	3	,	,	PUNCT
ejpam-6178	12	4	the	the	DET
ejpam-6178	12	5	dual	dual	ADJ
ejpam-6178	12	6	of	of	ADP
ejpam-6178	12	7	the	the	DET
ejpam-6178	12	8	b	b	NOUN
ejpam-6178	12	9	-	-	PUNCT
ejpam-6178	12	10	algebras	algebras	PROPN
ejpam-6178	12	11	was	be	AUX
ejpam-6178	12	12	initiated	initiate	VERB
ejpam-6178	12	13	by	by	ADP
ejpam-6178	12	14	k.	k.	PROPN
ejpam-6178	12	15	belleza	belleza	PROPN
ejpam-6178	12	16	and	and	CCONJ
ejpam-6178	12	17	j.r	j.r	PROPN
ejpam-6178	12	18	.	.	PROPN
ejpam-6178	12	19	albaracin	albaracin	PROPN
ejpam-6178	12	20	and	and	CCONJ
ejpam-6178	12	21	some	some	PRON
ejpam-6178	12	22	of	of	ADP
ejpam-6178	12	23	its	its	PRON
ejpam-6178	12	24	special	special	ADJ
ejpam-6178	12	25	subsets	subset	NOUN
ejpam-6178	12	26	,	,	PUNCT
ejpam-6178	12	27	namely	namely	ADV
ejpam-6178	12	28	,	,	PUNCT
ejpam-6178	12	29	the	the	DET
ejpam-6178	12	30	dual	dual	ADJ
ejpam-6178	12	31	b	b	NOUN
ejpam-6178	12	32	-	-	PUNCT
ejpam-6178	12	33	subalgebra	subalgebra	NOUN
ejpam-6178	12	34	,	,	PUNCT
ejpam-6178	12	35	dual	dual	ADJ
ejpam-6178	12	36	b	b	NOUN
ejpam-6178	12	37	-	-	PUNCT
ejpam-6178	12	38	filters	filter	NOUN
ejpam-6178	12	39	,	,	PUNCT
ejpam-6178	12	40	and	and	CCONJ
ejpam-6178	12	41	normal	normal	ADJ
ejpam-6178	12	42	subsets	subset	NOUN
ejpam-6178	12	43	.	.	PUNCT
ejpam-6178	13	1	moreover	moreover	ADV
ejpam-6178	13	2	,	,	PUNCT
ejpam-6178	13	3	the	the	DET
ejpam-6178	13	4	researchers	researcher	NOUN
ejpam-6178	13	5	constructed	construct	VERB
ejpam-6178	13	6	a	a	DET
ejpam-6178	13	7	congruence	congruence	NOUN
ejpam-6178	13	8	relation	relation	NOUN
ejpam-6178	13	9	on	on	ADP
ejpam-6178	13	10	a	a	DET
ejpam-6178	13	11	dual	dual	ADJ
ejpam-6178	13	12	b	b	NOUN
ejpam-6178	13	13	-	-	PUNCT
ejpam-6178	13	14	algebra	algebra	NOUN
ejpam-6178	13	15	[	[	X
ejpam-6178	13	16	10	10	NUM
ejpam-6178	13	17	]	]	PUNCT
ejpam-6178	13	18	.	.	PUNCT
ejpam-6178	14	1	the	the	DET
ejpam-6178	14	2	normal	normal	ADJ
ejpam-6178	14	3	dual	dual	ADJ
ejpam-6178	14	4	b	b	NOUN
ejpam-6178	14	5	-	-	PUNCT
ejpam-6178	14	6	subalgebra	subalgebra	ADJ
ejpam-6178	14	7	and	and	CCONJ
ejpam-6178	14	8	congruence	congruence	PROPN
ejpam-6178	14	9	relation	relation	NOUN
ejpam-6178	14	10	were	be	AUX
ejpam-6178	14	11	used	use	VERB
ejpam-6178	14	12	by	by	ADP
ejpam-6178	14	13	j.e	j.e	PROPN
ejpam-6178	14	14	bolima	bolima	NOUN
ejpam-6178	14	15	and	and	CCONJ
ejpam-6178	14	16	k.b	k.b	PROPN
ejpam-6178	14	17	.	.	PROPN
ejpam-6178	15	1	fuentes	fuentes	PROPN
ejpam-6178	15	2	to	to	PART
ejpam-6178	15	3	form	form	VERB
ejpam-6178	15	4	the	the	DET
ejpam-6178	15	5	quotient	quotient	NOUN
ejpam-6178	15	6	dual	dual	ADJ
ejpam-6178	15	7	b	b	NOUN
ejpam-6178	15	8	-	-	PUNCT
ejpam-6178	15	9	algebra	algebra	NOUN
ejpam-6178	15	10	and	and	CCONJ
ejpam-6178	15	11	the	the	DET
ejpam-6178	15	12	homomorphism	homomorphism	NOUN
ejpam-6178	15	13	map	map	NOUN
ejpam-6178	15	14	from	from	ADP
ejpam-6178	15	15	a	a	DET
ejpam-6178	15	16	dual	dual	ADJ
ejpam-6178	15	17	b	b	NOUN
ejpam-6178	15	18	-	-	PUNCT
ejpam-6178	15	19	algebra	algebra	NOUN
ejpam-6178	15	20	to	to	ADP
ejpam-6178	15	21	a	a	DET
ejpam-6178	15	22	quotient	quotient	NOUN
ejpam-6178	15	23	dual	dual	ADJ
ejpam-6178	15	24	b	b	NOUN
ejpam-6178	15	25	-	-	PUNCT
ejpam-6178	15	26	algebra	algebra	NOUN
ejpam-6178	15	27	.	.	PUNCT
ejpam-6178	16	1	the	the	DET
ejpam-6178	16	2	properties	property	NOUN
ejpam-6178	16	3	of	of	ADP
ejpam-6178	16	4	this	this	DET
ejpam-6178	16	5	mapping	mapping	NOUN
ejpam-6178	16	6	were	be	AUX
ejpam-6178	16	7	also	also	ADV
ejpam-6178	16	8	obtained	obtain	VERB
ejpam-6178	16	9	[	[	PUNCT
ejpam-6178	16	10	11	11	NUM
ejpam-6178	16	11	]	]	PUNCT
ejpam-6178	16	12	.	.	PUNCT
ejpam-6178	17	1	several	several	ADJ
ejpam-6178	17	2	studies	study	NOUN
ejpam-6178	17	3	on	on	ADP
ejpam-6178	17	4	establishing	establish	VERB
ejpam-6178	17	5	the	the	DET
ejpam-6178	17	6	homomorphism	homomorphism	PROPN
ejpam-6178	17	7	maps	map	NOUN
ejpam-6178	17	8	from	from	ADP
ejpam-6178	17	9	a	a	DET
ejpam-6178	17	10	type	type	NOUN
ejpam-6178	17	11	(	(	PUNCT
ejpam-6178	17	12	2,0	2,0	NUM
ejpam-6178	17	13	)	)	PUNCT
ejpam-6178	17	14	algebras	algebra	NOUN
ejpam-6178	17	15	to	to	ADP
ejpam-6178	17	16	their	their	PRON
ejpam-6178	17	17	respective	respective	ADJ
ejpam-6178	17	18	quotient	quotient	NOUN
ejpam-6178	17	19	type	type	NOUN
ejpam-6178	17	20	(	(	PUNCT
ejpam-6178	17	21	2,0	2,0	NUM
ejpam-6178	17	22	)	)	PUNCT
ejpam-6178	17	23	algebras	algebra	NOUN
ejpam-6178	17	24	using	use	VERB
ejpam-6178	17	25	ideals	ideal	NOUN
ejpam-6178	17	26	have	have	AUX
ejpam-6178	17	27	been	be	AUX
ejpam-6178	17	28	noted	note	VERB
ejpam-6178	17	29	(	(	PUNCT
ejpam-6178	17	30	see	see	VERB
ejpam-6178	17	31	[	[	X
ejpam-6178	17	32	12	12	NUM
ejpam-6178	17	33	]	]	PUNCT
ejpam-6178	17	34	,	,	PUNCT
ejpam-6178	18	1	[	[	X
ejpam-6178	18	2	13	13	NUM
ejpam-6178	18	3	]	]	PUNCT
ejpam-6178	18	4	,	,	PUNCT
ejpam-6178	18	5	∗corresponding	∗corresponde	VERB
ejpam-6178	18	6	author	author	NOUN
ejpam-6178	18	7	.	.	PUNCT
ejpam-6178	19	1	doi	doi	NOUN
ejpam-6178	19	2	:	:	PUNCT
ejpam-6178	19	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6178	https://doi.org/10.29020/nybg.ejpam.v18i4.6178	ADV
ejpam-6178	19	4	email	email	NOUN
ejpam-6178	19	5	addresses	address	NOUN
ejpam-6178	19	6	:	:	PUNCT
ejpam-6178	19	7	rashinn37@gmail.com	rashinn37@gmail.com	X
ejpam-6178	19	8	(	(	PUNCT
ejpam-6178	19	9	r.	r.	PROPN
ejpam-6178	19	10	nuñez	nuñez	PROPN
ejpam-6178	19	11	)	)	PUNCT
ejpam-6178	19	12	,	,	PUNCT
ejpam-6178	19	13	kebelleza@usc.edu.ph	kebelleza@usc.edu.ph	PROPN
ejpam-6178	19	14	(	(	PUNCT
ejpam-6178	19	15	k.	k.	PROPN
ejpam-6178	19	16	b.	b.	PROPN
ejpam-6178	19	17	fuentes	fuentes	PROPN
ejpam-6178	19	18	)	)	PUNCT
ejpam-6178	19	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6178	20	1	1	1	NUM
ejpam-6178	20	2	copyright	copyright	NOUN
ejpam-6178	20	3	:	:	PUNCT
ejpam-6178	20	4	©	©	PROPN
ejpam-6178	20	5	2025	2025	NUM
ejpam-6178	20	6	the	the	DET
ejpam-6178	20	7	author(s	author(s	NOUN
ejpam-6178	20	8	)	)	PUNCT
ejpam-6178	20	9	.	.	PUNCT
ejpam-6178	21	1	(	(	PUNCT
ejpam-6178	21	2	cc	cc	NOUN
ejpam-6178	21	3	by	by	ADP
ejpam-6178	21	4	-	-	PUNCT
ejpam-6178	21	5	nc	nc	PROPN
ejpam-6178	21	6	4.0	4.0	NUM
ejpam-6178	21	7	)	)	PUNCT
ejpam-6178	21	8	r.	r.	PROPN
ejpam-6178	21	9	nuñez	nuñez	PROPN
ejpam-6178	21	10	,	,	PUNCT
ejpam-6178	21	11	k.	k.	PROPN
ejpam-6178	21	12	b.	b.	PROPN
ejpam-6178	21	13	fuentes	fuentes	PROPN
ejpam-6178	21	14	/	/	SYM
ejpam-6178	21	15	eur	eur	PROPN
ejpam-6178	21	16	.	.	PUNCT
ejpam-6178	22	1	j.	j.	PROPN
ejpam-6178	22	2	pure	pure	PROPN
ejpam-6178	22	3	appl	appl	PROPN
ejpam-6178	22	4	.	.	PROPN
ejpam-6178	22	5	math	math	PROPN
ejpam-6178	22	6	,	,	PUNCT
ejpam-6178	22	7	18	18	NUM
ejpam-6178	22	8	(	(	PUNCT
ejpam-6178	22	9	4	4	NUM
ejpam-6178	22	10	)	)	PUNCT
ejpam-6178	22	11	(	(	PUNCT
ejpam-6178	22	12	2025	2025	NUM
ejpam-6178	22	13	)	)	PUNCT
ejpam-6178	22	14	,	,	PUNCT
ejpam-6178	22	15	6178	6178	NUM
ejpam-6178	22	16	2	2	NUM
ejpam-6178	22	17	of	of	ADP
ejpam-6178	22	18	15	15	NUM
ejpam-6178	22	19	[	[	X
ejpam-6178	22	20	4	4	NUM
ejpam-6178	22	21	]	]	PUNCT
ejpam-6178	22	22	,	,	PUNCT
ejpam-6178	22	23	[	[	X
ejpam-6178	22	24	14	14	NUM
ejpam-6178	22	25	]	]	SYM
ejpam-6178	22	26	)	)	PUNCT
ejpam-6178	22	27	.	.	PUNCT
ejpam-6178	23	1	remarkably	remarkably	ADV
ejpam-6178	23	2	,	,	PUNCT
ejpam-6178	23	3	in	in	ADP
ejpam-6178	23	4	[	[	X
ejpam-6178	23	5	8	8	NUM
ejpam-6178	23	6	]	]	X
ejpam-6178	23	7	the	the	DET
ejpam-6178	23	8	canonical	canonical	ADJ
ejpam-6178	23	9	projection	projection	NOUN
ejpam-6178	23	10	from	from	ADP
ejpam-6178	23	11	a	a	DET
ejpam-6178	23	12	b	b	NOUN
ejpam-6178	23	13	-	-	PUNCT
ejpam-6178	23	14	algebra	algebra	NOUN
ejpam-6178	23	15	to	to	ADP
ejpam-6178	23	16	the	the	DET
ejpam-6178	23	17	quotient	quotient	NOUN
ejpam-6178	23	18	balgebra	balgebra	NOUN
ejpam-6178	23	19	was	be	AUX
ejpam-6178	23	20	used	use	VERB
ejpam-6178	23	21	to	to	PART
ejpam-6178	23	22	prove	prove	VERB
ejpam-6178	23	23	some	some	DET
ejpam-6178	23	24	isomorphism	isomorphism	NOUN
ejpam-6178	23	25	theorems	theorem	NOUN
ejpam-6178	23	26	.	.	PUNCT
ejpam-6178	24	1	moreover	moreover	ADV
ejpam-6178	24	2	,	,	PUNCT
ejpam-6178	24	3	this	this	DET
ejpam-6178	24	4	canonical	canonical	ADJ
ejpam-6178	24	5	projection	projection	NOUN
ejpam-6178	24	6	map	map	NOUN
ejpam-6178	24	7	was	be	AUX
ejpam-6178	24	8	also	also	ADV
ejpam-6178	24	9	used	use	VERB
ejpam-6178	24	10	to	to	PART
ejpam-6178	24	11	prove	prove	VERB
ejpam-6178	24	12	some	some	DET
ejpam-6178	24	13	fundamental	fundamental	ADJ
ejpam-6178	24	14	properties	property	NOUN
ejpam-6178	24	15	of	of	ADP
ejpam-6178	24	16	the	the	DET
ejpam-6178	24	17	topological	topological	ADJ
ejpam-6178	24	18	b	b	NOUN
ejpam-6178	24	19	-	-	PUNCT
ejpam-6178	24	20	algebra	algebra	NOUN
ejpam-6178	24	21	,	,	PUNCT
ejpam-6178	24	22	which	which	PRON
ejpam-6178	24	23	is	be	AUX
ejpam-6178	24	24	a	a	DET
ejpam-6178	24	25	b	b	NOUN
ejpam-6178	24	26	-	-	PUNCT
ejpam-6178	24	27	algebra	algebra	NOUN
ejpam-6178	24	28	equipped	equip	VERB
ejpam-6178	24	29	with	with	ADP
ejpam-6178	24	30	a	a	DET
ejpam-6178	24	31	topology	topology	NOUN
ejpam-6178	24	32	that	that	PRON
ejpam-6178	24	33	makes	make	VERB
ejpam-6178	24	34	the	the	DET
ejpam-6178	24	35	binary	binary	ADJ
ejpam-6178	24	36	operation	operation	NOUN
ejpam-6178	24	37	of	of	ADP
ejpam-6178	24	38	the	the	DET
ejpam-6178	24	39	b	b	NOUN
ejpam-6178	24	40	-	-	PUNCT
ejpam-6178	24	41	algebra	algebra	NOUN
ejpam-6178	24	42	continuous	continuous	ADJ
ejpam-6178	24	43	[	[	X
ejpam-6178	24	44	15	15	NUM
ejpam-6178	24	45	]	]	PUNCT
ejpam-6178	24	46	.	.	PUNCT
ejpam-6178	25	1	furthermore	furthermore	ADV
ejpam-6178	25	2	,	,	PUNCT
ejpam-6178	25	3	hoo	hoo	INTJ
ejpam-6178	25	4	in	in	ADP
ejpam-6178	25	5	his	his	PRON
ejpam-6178	25	6	study	study	NOUN
ejpam-6178	25	7	on	on	ADP
ejpam-6178	25	8	topological	topological	ADJ
ejpam-6178	25	9	mv	mv	PROPN
ejpam-6178	25	10	-algebra	-algebra	PROPN
ejpam-6178	25	11	use	use	VERB
ejpam-6178	25	12	the	the	DET
ejpam-6178	25	13	homomorphism	homomorphism	NOUN
ejpam-6178	25	14	map	map	NOUN
ejpam-6178	25	15	from	from	ADP
ejpam-6178	25	16	a	a	DET
ejpam-6178	25	17	mv	mv	PROPN
ejpam-6178	25	18	-algebra	-algebra	NOUN
ejpam-6178	25	19	to	to	ADP
ejpam-6178	25	20	a	a	DET
ejpam-6178	25	21	quotient	quotient	NOUN
ejpam-6178	25	22	mv	mv	PROPN
ejpam-6178	25	23	-algebra	-algebra	PROPN
ejpam-6178	25	24	(	(	PUNCT
ejpam-6178	25	25	determined	determine	VERB
ejpam-6178	25	26	by	by	ADP
ejpam-6178	25	27	a	a	DET
ejpam-6178	25	28	mv	mv	PROPN
ejpam-6178	25	29	-ideal	-ideal	NOUN
ejpam-6178	25	30	)	)	PUNCT
ejpam-6178	25	31	to	to	PART
ejpam-6178	25	32	study	study	VERB
ejpam-6178	25	33	on	on	ADP
ejpam-6178	25	34	topological	topological	ADJ
ejpam-6178	25	35	homomorphisms	homomorphism	NOUN
ejpam-6178	25	36	[	[	X
ejpam-6178	25	37	14	14	NUM
ejpam-6178	25	38	]	]	PUNCT
ejpam-6178	25	39	.	.	PUNCT
ejpam-6178	26	1	moreover	moreover	ADV
ejpam-6178	26	2	,	,	PUNCT
ejpam-6178	26	3	a.	a.	PROPN
ejpam-6178	26	4	satirad	satirad	PROPN
ejpam-6178	26	5	and	and	CCONJ
ejpam-6178	26	6	a.	a.	NOUN
ejpam-6178	26	7	iampan	iampan	PROPN
ejpam-6178	26	8	use	use	VERB
ejpam-6178	26	9	this	this	DET
ejpam-6178	26	10	kind	kind	NOUN
ejpam-6178	26	11	of	of	ADP
ejpam-6178	26	12	homomorphism	homomorphism	NOUN
ejpam-6178	26	13	map	map	NOUN
ejpam-6178	26	14	to	to	PART
ejpam-6178	26	15	study	study	VERB
ejpam-6178	26	16	on	on	ADP
ejpam-6178	26	17	topological	topological	ADJ
ejpam-6178	26	18	homomorphisms	homomorphism	NOUN
ejpam-6178	26	19	in	in	ADP
ejpam-6178	26	20	a	a	DET
ejpam-6178	26	21	topological	topological	ADJ
ejpam-6178	26	22	up	up	ADV
ejpam-6178	26	23	-algebra	-algebra	PROPN
ejpam-6178	26	24	[	[	X
ejpam-6178	26	25	16	16	NUM
ejpam-6178	26	26	]	]	PUNCT
ejpam-6178	26	27	.	.	PUNCT
ejpam-6178	27	1	this	this	DET
ejpam-6178	27	2	study	study	NOUN
ejpam-6178	27	3	aimed	aim	VERB
ejpam-6178	27	4	to	to	PART
ejpam-6178	27	5	establish	establish	VERB
ejpam-6178	27	6	the	the	DET
ejpam-6178	27	7	topological	topological	ADJ
ejpam-6178	27	8	homomorphism	homomorphism	NOUN
ejpam-6178	27	9	in	in	ADP
ejpam-6178	27	10	a	a	DET
ejpam-6178	27	11	topological	topological	ADJ
ejpam-6178	27	12	dual	dual	ADJ
ejpam-6178	27	13	b	b	NOUN
ejpam-6178	27	14	-	-	PUNCT
ejpam-6178	27	15	algebra	algebra	NOUN
ejpam-6178	27	16	and	and	CCONJ
ejpam-6178	27	17	its	its	PRON
ejpam-6178	27	18	properties	property	NOUN
ejpam-6178	27	19	using	use	VERB
ejpam-6178	27	20	the	the	DET
ejpam-6178	27	21	natural	natural	ADJ
ejpam-6178	27	22	dual	dual	ADJ
ejpam-6178	27	23	b	b	NOUN
ejpam-6178	27	24	-	-	PUNCT
ejpam-6178	27	25	homomorphism	homomorphism	NOUN
ejpam-6178	27	26	.	.	PUNCT
ejpam-6178	28	1	findings	finding	NOUN
ejpam-6178	28	2	of	of	ADP
ejpam-6178	28	3	this	this	DET
ejpam-6178	28	4	research	research	NOUN
ejpam-6178	28	5	expanded	expand	VERB
ejpam-6178	28	6	some	some	DET
ejpam-6178	28	7	concepts	concept	NOUN
ejpam-6178	28	8	in	in	ADP
ejpam-6178	28	9	topology	topology	NOUN
ejpam-6178	28	10	such	such	ADJ
ejpam-6178	28	11	as	as	ADP
ejpam-6178	28	12	properties	property	NOUN
ejpam-6178	28	13	of	of	ADP
ejpam-6178	28	14	a	a	DET
ejpam-6178	28	15	topological	topological	ADJ
ejpam-6178	28	16	spaces	space	NOUN
ejpam-6178	28	17	and	and	CCONJ
ejpam-6178	28	18	mappings	mapping	NOUN
ejpam-6178	28	19	between	between	ADP
ejpam-6178	28	20	topological	topological	ADJ
ejpam-6178	28	21	spaces	space	NOUN
ejpam-6178	28	22	.	.	PUNCT
ejpam-6178	29	1	since	since	SCONJ
ejpam-6178	29	2	the	the	DET
ejpam-6178	29	3	tdb	tdb	PROPN
ejpam-6178	29	4	-	-	PROPN
ejpam-6178	29	5	homomorphism	homomorphism	NOUN
ejpam-6178	29	6	simultaneously	simultaneously	ADV
ejpam-6178	29	7	look	look	VERB
ejpam-6178	29	8	on	on	ADP
ejpam-6178	29	9	the	the	DET
ejpam-6178	29	10	algebraic	algebraic	ADJ
ejpam-6178	29	11	structure	structure	NOUN
ejpam-6178	29	12	and	and	CCONJ
ejpam-6178	29	13	topological	topological	ADJ
ejpam-6178	29	14	structure	structure	NOUN
ejpam-6178	29	15	of	of	ADP
ejpam-6178	29	16	the	the	DET
ejpam-6178	29	17	dual	dual	ADJ
ejpam-6178	29	18	b	b	NOUN
ejpam-6178	29	19	-	-	PUNCT
ejpam-6178	29	20	algebra	algebra	NOUN
ejpam-6178	29	21	,	,	PUNCT
ejpam-6178	29	22	future	future	ADJ
ejpam-6178	29	23	applications	application	NOUN
ejpam-6178	29	24	of	of	ADP
ejpam-6178	29	25	the	the	DET
ejpam-6178	29	26	study	study	NOUN
ejpam-6178	29	27	may	may	AUX
ejpam-6178	29	28	link	link	VERB
ejpam-6178	29	29	to	to	ADP
ejpam-6178	29	30	development	development	NOUN
ejpam-6178	29	31	of	of	ADP
ejpam-6178	29	32	logical	logical	ADJ
ejpam-6178	29	33	algebras	algebra	NOUN
ejpam-6178	29	34	,	,	PUNCT
ejpam-6178	29	35	algebraic	algebraic	ADJ
ejpam-6178	29	36	topology	topology	NOUN
ejpam-6178	29	37	or	or	CCONJ
ejpam-6178	29	38	other	other	ADJ
ejpam-6178	29	39	related	relate	VERB
ejpam-6178	29	40	fields	field	NOUN
ejpam-6178	29	41	which	which	PRON
ejpam-6178	29	42	studies	study	VERB
ejpam-6178	29	43	about	about	ADP
ejpam-6178	29	44	mappings	mapping	NOUN
ejpam-6178	29	45	on	on	ADP
ejpam-6178	29	46	a	a	DET
ejpam-6178	29	47	topological	topological	ADJ
ejpam-6178	29	48	structure	structure	NOUN
ejpam-6178	29	49	having	have	VERB
ejpam-6178	29	50	algebraic	algebraic	ADJ
ejpam-6178	29	51	properties	property	NOUN
ejpam-6178	29	52	.	.	PUNCT
ejpam-6178	30	1	the	the	DET
ejpam-6178	30	2	topological	topological	ADJ
ejpam-6178	30	3	isomorphism	isomorphism	NOUN
ejpam-6178	30	4	in	in	ADP
ejpam-6178	30	5	a	a	PRON
ejpam-6178	30	6	topological	topological	ADJ
ejpam-6178	30	7	dual	dual	ADJ
ejpam-6178	30	8	b	b	X
ejpam-6178	30	9	-	-	PUNCT
ejpam-6178	30	10	algebra	algebra	NOUN
ejpam-6178	30	11	was	be	AUX
ejpam-6178	30	12	also	also	ADV
ejpam-6178	30	13	initiated	initiate	VERB
ejpam-6178	30	14	.	.	PUNCT
ejpam-6178	31	1	2	2	X
ejpam-6178	31	2	.	.	X
ejpam-6178	31	3	preliminaries	preliminary	NOUN
ejpam-6178	31	4	definition	definition	NOUN
ejpam-6178	31	5	1	1	NUM
ejpam-6178	31	6	.	.	PUNCT
ejpam-6178	32	1	[	[	X
ejpam-6178	32	2	17	17	NUM
ejpam-6178	32	3	]	]	X
ejpam-6178	32	4	a	a	DET
ejpam-6178	32	5	dual	dual	ADJ
ejpam-6178	32	6	b	b	NOUN
ejpam-6178	32	7	-	-	PUNCT
ejpam-6178	32	8	algebra	algebra	NOUN
ejpam-6178	32	9	(	(	PUNCT
ejpam-6178	32	10	or	or	CCONJ
ejpam-6178	32	11	db	db	NOUN
ejpam-6178	32	12	-	-	PUNCT
ejpam-6178	32	13	algebra	algebra	NOUN
ejpam-6178	32	14	)	)	PUNCT
ejpam-6178	32	15	,	,	PUNCT
ejpam-6178	32	16	x	x	X
ejpam-6178	32	17	is	be	AUX
ejpam-6178	32	18	a	a	DET
ejpam-6178	32	19	triple	triple	ADJ
ejpam-6178	32	20	(	(	PUNCT
ejpam-6178	32	21	x	x	NOUN
ejpam-6178	32	22	,	,	PUNCT
ejpam-6178	32	23	◦	◦	NOUN
ejpam-6178	32	24	,	,	PUNCT
ejpam-6178	32	25	1	1	NUM
ejpam-6178	32	26	)	)	PUNCT
ejpam-6178	32	27	where	where	SCONJ
ejpam-6178	32	28	x	x	PRON
ejpam-6178	32	29	is	be	AUX
ejpam-6178	32	30	a	a	DET
ejpam-6178	32	31	nonempty	nonempty	ADV
ejpam-6178	32	32	set	set	VERB
ejpam-6178	32	33	with	with	ADP
ejpam-6178	32	34	a	a	DET
ejpam-6178	32	35	binary	binary	ADJ
ejpam-6178	32	36	operation	operation	NOUN
ejpam-6178	32	37	“	"	PUNCT
ejpam-6178	32	38	◦	◦	NOUN
ejpam-6178	32	39	”	"	PUNCT
ejpam-6178	32	40	and	and	CCONJ
ejpam-6178	32	41	a	a	DET
ejpam-6178	32	42	constant	constant	ADJ
ejpam-6178	32	43	1	1	NUM
ejpam-6178	32	44	satisfying	satisfy	VERB
ejpam-6178	32	45	the	the	DET
ejpam-6178	32	46	following	follow	VERB
ejpam-6178	32	47	axioms	axiom	NOUN
ejpam-6178	32	48	for	for	ADP
ejpam-6178	32	49	all	all	DET
ejpam-6178	32	50	x	x	NOUN
ejpam-6178	32	51	,	,	PUNCT
ejpam-6178	32	52	y	y	PROPN
ejpam-6178	32	53	,	,	PUNCT
ejpam-6178	32	54	z	z	VERB
ejpam-6178	32	55	in	in	ADP
ejpam-6178	32	56	x	x	NOUN
ejpam-6178	32	57	:	:	PUNCT
ejpam-6178	32	58	(	(	PUNCT
ejpam-6178	32	59	db1	db1	NOUN
ejpam-6178	32	60	)	)	PUNCT
ejpam-6178	32	61	x	x	SYM
ejpam-6178	33	1	◦	◦	NOUN
ejpam-6178	33	2	x	x	SYM
ejpam-6178	33	3	=	=	NOUN
ejpam-6178	33	4	1	1	NUM
ejpam-6178	33	5	;	;	PUNCT
ejpam-6178	33	6	(	(	PUNCT
ejpam-6178	33	7	db2	db2	NOUN
ejpam-6178	33	8	)	)	PUNCT
ejpam-6178	33	9	1	1	NUM
ejpam-6178	33	10	◦	◦	NOUN
ejpam-6178	33	11	x	x	SYM
ejpam-6178	33	12	=	=	SYM
ejpam-6178	33	13	x	x	X
ejpam-6178	33	14	;	;	PUNCT
ejpam-6178	33	15	(	(	PUNCT
ejpam-6178	33	16	db3	db3	PROPN
ejpam-6178	33	17	)	)	PUNCT
ejpam-6178	33	18	x	x	SYM
ejpam-6178	34	1	◦	◦	NOUN
ejpam-6178	34	2	(	(	PUNCT
ejpam-6178	34	3	y	y	PROPN
ejpam-6178	34	4	◦	◦	PROPN
ejpam-6178	34	5	z	z	PROPN
ejpam-6178	34	6	)	)	PUNCT
ejpam-6178	34	7	=	=	SYM
ejpam-6178	34	8	(	(	PUNCT
ejpam-6178	34	9	(	(	PUNCT
ejpam-6178	34	10	y	y	NOUN
ejpam-6178	34	11	◦	◦	NOUN
ejpam-6178	34	12	1	1	NUM
ejpam-6178	34	13	)	)	PUNCT
ejpam-6178	34	14	◦	◦	NOUN
ejpam-6178	34	15	x	x	SYM
ejpam-6178	34	16	)	)	PUNCT
ejpam-6178	34	17	◦	◦	NOUN
ejpam-6178	34	18	z.	z.	PROPN
ejpam-6178	34	19	example	example	NOUN
ejpam-6178	35	1	1	1	NUM
ejpam-6178	35	2	.	.	PUNCT
ejpam-6178	36	1	[	[	X
ejpam-6178	36	2	10	10	NUM
ejpam-6178	36	3	]	]	PUNCT
ejpam-6178	36	4	let	let	VERB
ejpam-6178	36	5	x	x	PUNCT
ejpam-6178	36	6	=	=	PRON
ejpam-6178	36	7	{	{	PUNCT
ejpam-6178	36	8	1	1	NUM
ejpam-6178	36	9	,	,	PUNCT
ejpam-6178	36	10	a	a	DET
ejpam-6178	36	11	,	,	PUNCT
ejpam-6178	36	12	b	b	NOUN
ejpam-6178	36	13	,	,	PUNCT
ejpam-6178	36	14	c	c	NOUN
ejpam-6178	36	15	}	}	PUNCT
ejpam-6178	36	16	with	with	ADP
ejpam-6178	36	17	the	the	DET
ejpam-6178	36	18	binary	binary	PROPN
ejpam-6178	36	19	operation	operation	NOUN
ejpam-6178	36	20	·	·	PUNCT
ejpam-6178	36	21	as	as	SCONJ
ejpam-6178	36	22	defined	define	VERB
ejpam-6178	36	23	in	in	ADP
ejpam-6178	36	24	the	the	DET
ejpam-6178	36	25	table	table	NOUN
ejpam-6178	36	26	:	:	PUNCT
ejpam-6178	36	27	◦	◦	NOUN
ejpam-6178	36	28	1	1	NUM
ejpam-6178	36	29	a	a	DET
ejpam-6178	36	30	b	b	NOUN
ejpam-6178	36	31	c	c	NOUN
ejpam-6178	36	32	1	1	NUM
ejpam-6178	36	33	1	1	NUM
ejpam-6178	36	34	a	a	DET
ejpam-6178	36	35	b	b	NOUN
ejpam-6178	36	36	c	c	ADP
ejpam-6178	36	37	a	a	DET
ejpam-6178	36	38	a	a	DET
ejpam-6178	36	39	1	1	NUM
ejpam-6178	36	40	c	c	NOUN
ejpam-6178	36	41	b	b	PROPN
ejpam-6178	36	42	b	b	PROPN
ejpam-6178	36	43	b	b	PROPN
ejpam-6178	36	44	c	c	PROPN
ejpam-6178	36	45	1	1	NUM
ejpam-6178	36	46	a	a	DET
ejpam-6178	36	47	c	c	NOUN
ejpam-6178	36	48	c	c	NOUN
ejpam-6178	36	49	b	b	PROPN
ejpam-6178	36	50	a	a	DET
ejpam-6178	36	51	1	1	NUM
ejpam-6178	36	52	then	then	ADV
ejpam-6178	36	53	(	(	PUNCT
ejpam-6178	36	54	x	x	NOUN
ejpam-6178	36	55	,	,	PUNCT
ejpam-6178	36	56	◦	◦	NOUN
ejpam-6178	36	57	,	,	PUNCT
ejpam-6178	36	58	1	1	NUM
ejpam-6178	36	59	)	)	PUNCT
ejpam-6178	36	60	is	be	AUX
ejpam-6178	36	61	a	a	DET
ejpam-6178	36	62	db	db	NOUN
ejpam-6178	36	63	-	-	PUNCT
ejpam-6178	36	64	algebra	algebra	NOUN
ejpam-6178	36	65	.	.	PUNCT
ejpam-6178	37	1	definition	definition	NOUN
ejpam-6178	37	2	2	2	NUM
ejpam-6178	37	3	.	.	PUNCT
ejpam-6178	38	1	[	[	X
ejpam-6178	38	2	10	10	NUM
ejpam-6178	38	3	]	]	PUNCT
ejpam-6178	38	4	let	let	VERB
ejpam-6178	38	5	x	x	PRON
ejpam-6178	38	6	be	be	AUX
ejpam-6178	38	7	a	a	DET
ejpam-6178	38	8	db	db	NOUN
ejpam-6178	38	9	-	-	PUNCT
ejpam-6178	38	10	algebra	algebra	NOUN
ejpam-6178	38	11	and	and	CCONJ
ejpam-6178	38	12	s	s	VERB
ejpam-6178	38	13	a	a	DET
ejpam-6178	38	14	nonempty	nonempty	ADJ
ejpam-6178	38	15	subset	subset	NOUN
ejpam-6178	38	16	of	of	ADP
ejpam-6178	38	17	x.	x.	NOUN
ejpam-6178	38	18	then	then	ADV
ejpam-6178	38	19	s	s	VERB
ejpam-6178	38	20	is	be	AUX
ejpam-6178	38	21	called	call	VERB
ejpam-6178	38	22	a	a	DET
ejpam-6178	38	23	dual	dual	ADJ
ejpam-6178	38	24	b	b	NOUN
ejpam-6178	38	25	-	-	PUNCT
ejpam-6178	38	26	subalgebra	subalgebra	NOUN
ejpam-6178	38	27	,	,	PUNCT
ejpam-6178	38	28	(	(	PUNCT
ejpam-6178	38	29	or	or	CCONJ
ejpam-6178	38	30	db	db	NOUN
ejpam-6178	38	31	-	-	PUNCT
ejpam-6178	38	32	subalgebra	subalgebra	NOUN
ejpam-6178	38	33	)	)	PUNCT
ejpam-6178	38	34	,	,	PUNCT
ejpam-6178	38	35	of	of	ADP
ejpam-6178	38	36	x	x	PRON
ejpam-6178	38	37	if	if	SCONJ
ejpam-6178	38	38	s	s	PRON
ejpam-6178	38	39	itself	itself	PRON
ejpam-6178	38	40	is	be	AUX
ejpam-6178	38	41	a	a	DET
ejpam-6178	38	42	db	db	NOUN
ejpam-6178	38	43	-	-	PUNCT
ejpam-6178	38	44	algebra	algebra	NOUN
ejpam-6178	38	45	with	with	ADP
ejpam-6178	38	46	binary	binary	ADJ
ejpam-6178	38	47	operation	operation	NOUN
ejpam-6178	38	48	of	of	ADP
ejpam-6178	38	49	x	x	PUNCT
ejpam-6178	38	50	on	on	ADP
ejpam-6178	38	51	s.	s.	PROPN
ejpam-6178	38	52	definition	definition	NOUN
ejpam-6178	38	53	3	3	NUM
ejpam-6178	38	54	.	.	PUNCT
ejpam-6178	39	1	[	[	X
ejpam-6178	39	2	10	10	NUM
ejpam-6178	39	3	]	]	PUNCT
ejpam-6178	39	4	let	let	VERB
ejpam-6178	39	5	x	x	PRON
ejpam-6178	39	6	be	be	AUX
ejpam-6178	39	7	a	a	DET
ejpam-6178	39	8	db	db	NOUN
ejpam-6178	39	9	-	-	PUNCT
ejpam-6178	39	10	algebra	algebra	NOUN
ejpam-6178	39	11	and	and	CCONJ
ejpam-6178	39	12	n	n	DET
ejpam-6178	39	13	a	a	DET
ejpam-6178	39	14	nonempty	nonempty	NOUN
ejpam-6178	39	15	subset	subset	NOUN
ejpam-6178	39	16	of	of	ADP
ejpam-6178	39	17	x.	x.	NOUN
ejpam-6178	39	18	then	then	ADV
ejpam-6178	39	19	n	n	PRON
ejpam-6178	39	20	is	be	AUX
ejpam-6178	39	21	a	a	DET
ejpam-6178	39	22	normal	normal	ADJ
ejpam-6178	39	23	subset	subset	NOUN
ejpam-6178	39	24	of	of	ADP
ejpam-6178	39	25	x	x	PRON
ejpam-6178	39	26	if	if	SCONJ
ejpam-6178	39	27	for	for	ADP
ejpam-6178	39	28	any	any	DET
ejpam-6178	39	29	a	a	DET
ejpam-6178	39	30	◦	◦	NOUN
ejpam-6178	39	31	b	b	NUM
ejpam-6178	39	32	,	,	PUNCT
ejpam-6178	39	33	x	x	PUNCT
ejpam-6178	39	34	◦	◦	VERB
ejpam-6178	39	35	y	y	PROPN
ejpam-6178	39	36	∈	∈	PROPN
ejpam-6178	39	37	n	n	CCONJ
ejpam-6178	39	38	,	,	PUNCT
ejpam-6178	39	39	(	(	PUNCT
ejpam-6178	39	40	a	a	DET
ejpam-6178	39	41	◦	◦	NOUN
ejpam-6178	39	42	x	x	NOUN
ejpam-6178	39	43	)	)	PUNCT
ejpam-6178	39	44	◦	◦	NOUN
ejpam-6178	39	45	(	(	PUNCT
ejpam-6178	39	46	b	b	X
ejpam-6178	39	47	◦	◦	NOUN
ejpam-6178	39	48	y	y	NOUN
ejpam-6178	39	49	)	)	PUNCT
ejpam-6178	39	50	∈	∈	PROPN
ejpam-6178	39	51	n	n	NOUN
ejpam-6178	39	52	.	.	PUNCT
ejpam-6178	40	1	a	a	DET
ejpam-6178	40	2	db	db	ADJ
ejpam-6178	40	3	-	-	PUNCT
ejpam-6178	40	4	subalgebra	subalgebra	NOUN
ejpam-6178	40	5	s	s	NOUN
ejpam-6178	40	6	of	of	ADP
ejpam-6178	40	7	a	a	DET
ejpam-6178	40	8	db	db	NOUN
ejpam-6178	40	9	-	-	PUNCT
ejpam-6178	40	10	algebra	algebra	NOUN
ejpam-6178	40	11	x	x	PUNCT
ejpam-6178	40	12	is	be	AUX
ejpam-6178	40	13	called	call	VERB
ejpam-6178	40	14	a	a	DET
ejpam-6178	40	15	normal	normal	ADJ
ejpam-6178	40	16	db	db	NOUN
ejpam-6178	40	17	-	-	PUNCT
ejpam-6178	40	18	subalgebra	subalgebra	NOUN
ejpam-6178	40	19	if	if	SCONJ
ejpam-6178	40	20	s	s	VERB
ejpam-6178	40	21	is	be	AUX
ejpam-6178	40	22	a	a	DET
ejpam-6178	40	23	normal	normal	ADJ
ejpam-6178	40	24	subset	subset	NOUN
ejpam-6178	40	25	of	of	ADP
ejpam-6178	40	26	x.	x.	PROPN
ejpam-6178	40	27	r.	r.	PROPN
ejpam-6178	40	28	nuñez	nuñez	PROPN
ejpam-6178	40	29	,	,	PUNCT
ejpam-6178	40	30	k.	k.	PROPN
ejpam-6178	40	31	b.	b.	PROPN
ejpam-6178	40	32	fuentes	fuentes	PROPN
ejpam-6178	40	33	/	/	SYM
ejpam-6178	40	34	eur	eur	PROPN
ejpam-6178	40	35	.	.	PUNCT
ejpam-6178	41	1	j.	j.	PROPN
ejpam-6178	41	2	pure	pure	PROPN
ejpam-6178	41	3	appl	appl	PROPN
ejpam-6178	41	4	.	.	PROPN
ejpam-6178	41	5	math	math	PROPN
ejpam-6178	41	6	,	,	PUNCT
ejpam-6178	41	7	18	18	NUM
ejpam-6178	41	8	(	(	PUNCT
ejpam-6178	41	9	4	4	NUM
ejpam-6178	41	10	)	)	PUNCT
ejpam-6178	41	11	(	(	PUNCT
ejpam-6178	41	12	2025	2025	NUM
ejpam-6178	41	13	)	)	PUNCT
ejpam-6178	41	14	,	,	PUNCT
ejpam-6178	41	15	6178	6178	NUM
ejpam-6178	41	16	3	3	NUM
ejpam-6178	41	17	of	of	ADP
ejpam-6178	41	18	15	15	NUM
ejpam-6178	41	19	theorem	theorem	NOUN
ejpam-6178	41	20	1	1	NUM
ejpam-6178	41	21	.	.	PUNCT
ejpam-6178	42	1	[	[	X
ejpam-6178	42	2	10	10	NUM
ejpam-6178	42	3	]	]	X
ejpam-6178	42	4	let	let	VERB
ejpam-6178	42	5	(	(	PUNCT
ejpam-6178	42	6	x	x	NOUN
ejpam-6178	42	7	,	,	PUNCT
ejpam-6178	42	8	◦	◦	NOUN
ejpam-6178	42	9	,	,	PUNCT
ejpam-6178	42	10	1	1	NUM
ejpam-6178	42	11	)	)	PUNCT
ejpam-6178	42	12	be	be	AUX
ejpam-6178	42	13	a	a	DET
ejpam-6178	42	14	db	db	NOUN
ejpam-6178	42	15	-	-	PUNCT
ejpam-6178	42	16	algebra	algebra	NOUN
ejpam-6178	42	17	and	and	CCONJ
ejpam-6178	42	18	s	s	VERB
ejpam-6178	42	19	a	a	DET
ejpam-6178	42	20	normal	normal	ADJ
ejpam-6178	42	21	db	db	NOUN
ejpam-6178	42	22	-	-	PUNCT
ejpam-6178	42	23	subalgebra	subalgebra	NOUN
ejpam-6178	42	24	of	of	ADP
ejpam-6178	42	25	x.	x.	NOUN
ejpam-6178	42	26	the	the	DET
ejpam-6178	42	27	relation	relation	NOUN
ejpam-6178	42	28	defined	define	VERB
ejpam-6178	42	29	by	by	ADP
ejpam-6178	42	30	x	x	X
ejpam-6178	42	31	∼	∼	NOUN
ejpam-6178	42	32	y	y	NOUN
ejpam-6178	42	33	if	if	SCONJ
ejpam-6178	42	34	and	and	CCONJ
ejpam-6178	42	35	only	only	ADV
ejpam-6178	42	36	if	if	SCONJ
ejpam-6178	42	37	x	x	PART
ejpam-6178	42	38	◦	◦	VERB
ejpam-6178	42	39	y	y	PROPN
ejpam-6178	42	40	,	,	PUNCT
ejpam-6178	42	41	y	y	PROPN
ejpam-6178	42	42	◦	◦	NOUN
ejpam-6178	42	43	x	x	X
ejpam-6178	42	44	∈	∈	NOUN
ejpam-6178	42	45	s	s	VERB
ejpam-6178	42	46	is	be	AUX
ejpam-6178	42	47	a	a	DET
ejpam-6178	42	48	congruence	congruence	NOUN
ejpam-6178	42	49	relation	relation	NOUN
ejpam-6178	42	50	on	on	ADP
ejpam-6178	42	51	x	x	PUNCT
ejpam-6178	42	52	for	for	ADP
ejpam-6178	42	53	any	any	DET
ejpam-6178	42	54	x	x	NOUN
ejpam-6178	42	55	,	,	PUNCT
ejpam-6178	42	56	y	y	PROPN
ejpam-6178	42	57	∈	∈	PROPN
ejpam-6178	42	58	x.	x.	NOUN
ejpam-6178	42	59	definition	definition	NOUN
ejpam-6178	42	60	4	4	NUM
ejpam-6178	42	61	.	.	PUNCT
ejpam-6178	43	1	[	[	X
ejpam-6178	43	2	10	10	NUM
ejpam-6178	43	3	]	]	X
ejpam-6178	43	4	let	let	VERB
ejpam-6178	43	5	(	(	PUNCT
ejpam-6178	43	6	x	x	NOUN
ejpam-6178	43	7	,	,	PUNCT
ejpam-6178	43	8	◦	◦	NOUN
ejpam-6178	43	9	,	,	PUNCT
ejpam-6178	43	10	1	1	NUM
ejpam-6178	43	11	)	)	PUNCT
ejpam-6178	43	12	be	be	AUX
ejpam-6178	43	13	a	a	DET
ejpam-6178	43	14	db	db	NOUN
ejpam-6178	43	15	-	-	PUNCT
ejpam-6178	43	16	algebra	algebra	NOUN
ejpam-6178	43	17	and	and	CCONJ
ejpam-6178	43	18	s	s	VERB
ejpam-6178	43	19	a	a	DET
ejpam-6178	43	20	normal	normal	ADJ
ejpam-6178	43	21	db	db	NOUN
ejpam-6178	43	22	-	-	PUNCT
ejpam-6178	43	23	subalgebra	subalgebra	NOUN
ejpam-6178	43	24	of	of	ADP
ejpam-6178	43	25	x.	x.	NOUN
ejpam-6178	43	26	define	define	VERB
ejpam-6178	43	27	a	a	DET
ejpam-6178	43	28	congruence	congruence	ADJ
ejpam-6178	43	29	class	class	NOUN
ejpam-6178	44	1	[	[	X
ejpam-6178	44	2	x]s	x]s	NOUN
ejpam-6178	44	3	by	by	ADP
ejpam-6178	44	4	[	[	X
ejpam-6178	44	5	x]s	x]s	PROPN
ejpam-6178	44	6	=	=	SYM
ejpam-6178	44	7	{	{	PUNCT
ejpam-6178	44	8	y	y	PROPN
ejpam-6178	44	9	∈	∈	PROPN
ejpam-6178	44	10	x|y	x|y	PUNCT
ejpam-6178	45	1	∼	∼	NOUN
ejpam-6178	45	2	x	x	SYM
ejpam-6178	45	3	}	}	PUNCT
ejpam-6178	45	4	and	and	CCONJ
ejpam-6178	45	5	define	define	VERB
ejpam-6178	45	6	x	x	NOUN
ejpam-6178	45	7	/	/	SYM
ejpam-6178	45	8	s	s	VERB
ejpam-6178	45	9	to	to	PART
ejpam-6178	45	10	be	be	AUX
ejpam-6178	45	11	the	the	DET
ejpam-6178	45	12	set	set	NOUN
ejpam-6178	45	13	of	of	ADP
ejpam-6178	45	14	all	all	DET
ejpam-6178	45	15	congruence	congruence	NOUN
ejpam-6178	45	16	classes	class	NOUN
ejpam-6178	45	17	of	of	ADP
ejpam-6178	45	18	x	x	PRON
ejpam-6178	45	19	,	,	PUNCT
ejpam-6178	45	20	that	that	PRON
ejpam-6178	45	21	is	be	AUX
ejpam-6178	45	22	x	x	X
ejpam-6178	45	23	/	/	SYM
ejpam-6178	45	24	s	s	PART
ejpam-6178	45	25	=	=	X
ejpam-6178	45	26	{	{	PUNCT
ejpam-6178	45	27	[	[	X
ejpam-6178	45	28	x]s	x]s	PROPN
ejpam-6178	45	29	|x	|x	X
ejpam-6178	45	30	∈	∈	PROPN
ejpam-6178	45	31	x	x	PUNCT
ejpam-6178	45	32	}	}	PUNCT
ejpam-6178	45	33	.	.	PUNCT
ejpam-6178	46	1	lemma	lemma	PROPN
ejpam-6178	46	2	1	1	NUM
ejpam-6178	46	3	.	.	PUNCT
ejpam-6178	47	1	[	[	X
ejpam-6178	47	2	11	11	NUM
ejpam-6178	47	3	]	]	PUNCT
ejpam-6178	47	4	.	.	PUNCT
ejpam-6178	48	1	let	let	VERB
ejpam-6178	48	2	s	s	PRON
ejpam-6178	48	3	be	be	AUX
ejpam-6178	48	4	a	a	DET
ejpam-6178	48	5	normal	normal	ADJ
ejpam-6178	48	6	db	db	NOUN
ejpam-6178	48	7	-	-	PUNCT
ejpam-6178	48	8	subalgebra	subalgebra	NOUN
ejpam-6178	48	9	of	of	ADP
ejpam-6178	48	10	a	a	DET
ejpam-6178	48	11	db	db	NOUN
ejpam-6178	48	12	-	-	PUNCT
ejpam-6178	48	13	algebra	algebra	NOUN
ejpam-6178	48	14	(	(	PUNCT
ejpam-6178	48	15	x	x	X
ejpam-6178	48	16	,	,	PUNCT
ejpam-6178	48	17	◦	◦	NOUN
ejpam-6178	48	18	,	,	PUNCT
ejpam-6178	48	19	1	1	NUM
ejpam-6178	48	20	)	)	PUNCT
ejpam-6178	48	21	and	and	CCONJ
ejpam-6178	48	22	x	x	X
ejpam-6178	48	23	,	,	PUNCT
ejpam-6178	48	24	y	y	PROPN
ejpam-6178	48	25	∈	∈	PROPN
ejpam-6178	48	26	x.	x.	NOUN
ejpam-6178	49	1	then	then	ADV
ejpam-6178	49	2	[	[	X
ejpam-6178	49	3	x]s	x]s	NOUN
ejpam-6178	49	4	=	=	PUNCT
ejpam-6178	50	1	[	[	X
ejpam-6178	50	2	y]s	y]s	X
ejpam-6178	50	3	if	if	SCONJ
ejpam-6178	50	4	and	and	CCONJ
ejpam-6178	50	5	only	only	ADV
ejpam-6178	50	6	if	if	SCONJ
ejpam-6178	50	7	x	x	PUNCT
ejpam-6178	50	8	∼	∼	NOUN
ejpam-6178	50	9	y.	y.	NOUN
ejpam-6178	50	10	theorem	theorem	VERB
ejpam-6178	50	11	2	2	NUM
ejpam-6178	50	12	.	.	PUNCT
ejpam-6178	51	1	[	[	X
ejpam-6178	51	2	11	11	NUM
ejpam-6178	51	3	]	]	PUNCT
ejpam-6178	51	4	let	let	VERB
ejpam-6178	51	5	s	s	PRON
ejpam-6178	51	6	be	be	AUX
ejpam-6178	51	7	a	a	DET
ejpam-6178	51	8	normal	normal	ADJ
ejpam-6178	51	9	db	db	NOUN
ejpam-6178	51	10	-	-	PUNCT
ejpam-6178	51	11	subalgebra	subalgebra	NOUN
ejpam-6178	51	12	of	of	ADP
ejpam-6178	51	13	a	a	DET
ejpam-6178	51	14	db	db	NOUN
ejpam-6178	51	15	-	-	PUNCT
ejpam-6178	51	16	algebra	algebra	NOUN
ejpam-6178	51	17	(	(	PUNCT
ejpam-6178	51	18	x	x	X
ejpam-6178	51	19	,	,	PUNCT
ejpam-6178	51	20	◦	◦	NOUN
ejpam-6178	51	21	,	,	PUNCT
ejpam-6178	51	22	1	1	NUM
ejpam-6178	51	23	)	)	PUNCT
ejpam-6178	51	24	.	.	PUNCT
ejpam-6178	52	1	then	then	ADV
ejpam-6178	52	2	(	(	PUNCT
ejpam-6178	52	3	x	x	X
ejpam-6178	52	4	/	/	SYM
ejpam-6178	52	5	s	s	PROPN
ejpam-6178	52	6	,	,	PUNCT
ejpam-6178	52	7	∗	∗	NOUN
ejpam-6178	52	8	,	,	PUNCT
ejpam-6178	52	9	[	[	X
ejpam-6178	52	10	1]s	1]s	NOUN
ejpam-6178	52	11	)	)	PUNCT
ejpam-6178	52	12	with	with	ADP
ejpam-6178	52	13	a	a	DET
ejpam-6178	52	14	binary	binary	ADJ
ejpam-6178	52	15	operation	operation	NOUN
ejpam-6178	52	16	∗	∗	NOUN
ejpam-6178	52	17	defined	define	VERB
ejpam-6178	52	18	by	by	ADP
ejpam-6178	52	19	[	[	X
ejpam-6178	52	20	x]s	x]s	PROPN
ejpam-6178	52	21	∗	∗	PROPN
ejpam-6178	52	22	[	[	X
ejpam-6178	52	23	y]s	y]s	X
ejpam-6178	52	24	=	=	PUNCT
ejpam-6178	53	1	[	[	X
ejpam-6178	53	2	x	x	X
ejpam-6178	53	3	∗	∗	NOUN
ejpam-6178	53	4	y]s	y]s	NOUN
ejpam-6178	53	5	for	for	ADP
ejpam-6178	53	6	all	all	DET
ejpam-6178	53	7	x	x	NOUN
ejpam-6178	53	8	,	,	PUNCT
ejpam-6178	53	9	y	y	PROPN
ejpam-6178	53	10	∈	∈	PROPN
ejpam-6178	53	11	x	x	X
ejpam-6178	53	12	is	be	AUX
ejpam-6178	53	13	a	a	DET
ejpam-6178	53	14	db	db	NOUN
ejpam-6178	53	15	-	-	PUNCT
ejpam-6178	53	16	algebra	algebra	NOUN
ejpam-6178	53	17	.	.	PUNCT
ejpam-6178	54	1	x	x	X
ejpam-6178	54	2	/	/	SYM
ejpam-6178	54	3	s	s	VERB
ejpam-6178	54	4	is	be	AUX
ejpam-6178	54	5	called	call	VERB
ejpam-6178	54	6	the	the	DET
ejpam-6178	54	7	quotient	quotient	NOUN
ejpam-6178	54	8	db	db	NOUN
ejpam-6178	54	9	-	-	PUNCT
ejpam-6178	54	10	algebra	algebra	NOUN
ejpam-6178	54	11	of	of	ADP
ejpam-6178	54	12	x	x	PUNCT
ejpam-6178	54	13	by	by	ADP
ejpam-6178	54	14	s.	s.	PROPN
ejpam-6178	54	15	definition	definition	NOUN
ejpam-6178	54	16	5	5	NUM
ejpam-6178	54	17	.	.	PUNCT
ejpam-6178	55	1	[	[	X
ejpam-6178	55	2	11	11	NUM
ejpam-6178	55	3	]	]	X
ejpam-6178	55	4	let	let	VERB
ejpam-6178	55	5	(	(	PUNCT
ejpam-6178	55	6	x	x	NOUN
ejpam-6178	55	7	,	,	PUNCT
ejpam-6178	55	8	◦	◦	NOUN
ejpam-6178	55	9	,	,	PUNCT
ejpam-6178	55	10	1x	1x	NUM
ejpam-6178	55	11	)	)	PUNCT
ejpam-6178	56	1	and	and	CCONJ
ejpam-6178	56	2	(	(	PUNCT
ejpam-6178	56	3	y	y	PROPN
ejpam-6178	56	4	,	,	PUNCT
ejpam-6178	56	5	∗	∗	NOUN
ejpam-6178	56	6	,	,	PUNCT
ejpam-6178	56	7	1y	1y	NOUN
ejpam-6178	56	8	)	)	PUNCT
ejpam-6178	56	9	be	be	AUX
ejpam-6178	56	10	db	db	NOUN
ejpam-6178	56	11	-	-	PUNCT
ejpam-6178	56	12	algebras	algebras	PROPN
ejpam-6178	56	13	.	.	PUNCT
ejpam-6178	57	1	a	a	DET
ejpam-6178	57	2	mapping	mapping	NOUN
ejpam-6178	57	3	φ	φ	NOUN
ejpam-6178	57	4	:	:	PUNCT
ejpam-6178	57	5	x	x	X
ejpam-6178	57	6	→	→	SYM
ejpam-6178	57	7	y	y	PROPN
ejpam-6178	57	8	is	be	AUX
ejpam-6178	57	9	called	call	VERB
ejpam-6178	57	10	a	a	DET
ejpam-6178	57	11	dual	dual	ADJ
ejpam-6178	57	12	b	b	NOUN
ejpam-6178	57	13	-	-	PUNCT
ejpam-6178	57	14	homomorphism	homomorphism	NOUN
ejpam-6178	57	15	(	(	PUNCT
ejpam-6178	57	16	or	or	CCONJ
ejpam-6178	57	17	db	db	NOUN
ejpam-6178	57	18	-	-	PUNCT
ejpam-6178	57	19	homomorphism	homomorphism	NOUN
ejpam-6178	57	20	)	)	PUNCT
ejpam-6178	57	21	,	,	PUNCT
ejpam-6178	57	22	from	from	ADP
ejpam-6178	57	23	x	x	PUNCT
ejpam-6178	57	24	into	into	ADP
ejpam-6178	57	25	y	y	PRON
ejpam-6178	57	26	if	if	SCONJ
ejpam-6178	57	27	φ(x	φ(x	PROPN
ejpam-6178	57	28	◦	◦	PROPN
ejpam-6178	57	29	y	y	NOUN
ejpam-6178	57	30	)	)	PUNCT
ejpam-6178	58	1	=	=	SYM
ejpam-6178	58	2	φ(x	φ(x	NOUN
ejpam-6178	58	3	)	)	PUNCT
ejpam-6178	58	4	∗	∗	NOUN
ejpam-6178	58	5	φ(y	φ(y	NOUN
ejpam-6178	58	6	)	)	PUNCT
ejpam-6178	58	7	for	for	ADP
ejpam-6178	58	8	any	any	DET
ejpam-6178	58	9	x	x	NOUN
ejpam-6178	58	10	,	,	PUNCT
ejpam-6178	58	11	y	y	PROPN
ejpam-6178	58	12	∈	∈	PROPN
ejpam-6178	58	13	x.	x.	NOUN
ejpam-6178	58	14	a	a	DET
ejpam-6178	58	15	db	db	PROPN
ejpam-6178	58	16	-	-	PUNCT
ejpam-6178	58	17	homomorphism	homomorphism	NOUN
ejpam-6178	58	18	φ	φ	PROPN
ejpam-6178	58	19	is	be	AUX
ejpam-6178	58	20	called	call	VERB
ejpam-6178	58	21	,	,	PUNCT
ejpam-6178	58	22	db	db	NOUN
ejpam-6178	58	23	-	-	PUNCT
ejpam-6178	58	24	monomorphism	monomorphism	NOUN
ejpam-6178	58	25	,	,	PUNCT
ejpam-6178	58	26	dbepimorphism	dbepimorphism	NOUN
ejpam-6178	58	27	,	,	PUNCT
ejpam-6178	58	28	or	or	CCONJ
ejpam-6178	58	29	db	db	PROPN
ejpam-6178	58	30	-	-	PUNCT
ejpam-6178	58	31	isomorphism	isomorphism	NOUN
ejpam-6178	58	32	,	,	PUNCT
ejpam-6178	58	33	if	if	SCONJ
ejpam-6178	58	34	φ	φ	PROPN
ejpam-6178	58	35	is	be	AUX
ejpam-6178	58	36	one	one	NUM
ejpam-6178	58	37	-	-	PUNCT
ejpam-6178	58	38	to	to	ADP
ejpam-6178	58	39	-	-	PUNCT
ejpam-6178	58	40	one	one	NUM
ejpam-6178	58	41	,	,	PUNCT
ejpam-6178	58	42	onto	onto	ADP
ejpam-6178	58	43	,	,	PUNCT
ejpam-6178	58	44	or	or	CCONJ
ejpam-6178	58	45	a	a	DET
ejpam-6178	58	46	bijection	bijection	NOUN
ejpam-6178	58	47	,	,	PUNCT
ejpam-6178	58	48	respectively	respectively	ADV
ejpam-6178	58	49	.	.	PUNCT
ejpam-6178	59	1	the	the	DET
ejpam-6178	59	2	kernel	kernel	NOUN
ejpam-6178	59	3	of	of	ADP
ejpam-6178	59	4	the	the	DET
ejpam-6178	59	5	db	db	PROPN
ejpam-6178	59	6	-	-	PUNCT
ejpam-6178	59	7	homomorphism	homomorphism	NOUN
ejpam-6178	59	8	φ	φ	NOUN
ejpam-6178	59	9	,	,	PUNCT
ejpam-6178	59	10	denoted	denote	VERB
ejpam-6178	59	11	by	by	ADP
ejpam-6178	59	12	kerφ	kerφ	PROPN
ejpam-6178	59	13	,	,	PUNCT
ejpam-6178	59	14	is	be	AUX
ejpam-6178	59	15	the	the	DET
ejpam-6178	59	16	set	set	NOUN
ejpam-6178	59	17	whose	whose	DET
ejpam-6178	59	18	elements	element	NOUN
ejpam-6178	59	19	of	of	ADP
ejpam-6178	59	20	x	x	SYM
ejpam-6178	59	21	are	be	AUX
ejpam-6178	59	22	map	map	NOUN
ejpam-6178	59	23	to	to	ADP
ejpam-6178	59	24	1y	1y	PROPN
ejpam-6178	59	25	.	.	PUNCT
ejpam-6178	60	1	theorem	theorem	ADJ
ejpam-6178	60	2	3	3	NUM
ejpam-6178	60	3	.	.	PUNCT
ejpam-6178	61	1	[	[	X
ejpam-6178	61	2	11	11	NUM
ejpam-6178	61	3	]	]	PUNCT
ejpam-6178	61	4	let	let	VERB
ejpam-6178	61	5	φ	φ	NOUN
ejpam-6178	61	6	:	:	PUNCT
ejpam-6178	61	7	x	x	X
ejpam-6178	61	8	→	→	SYM
ejpam-6178	61	9	y	y	X
ejpam-6178	61	10	be	be	AUX
ejpam-6178	61	11	a	a	DET
ejpam-6178	61	12	db	db	NOUN
ejpam-6178	61	13	-	-	PUNCT
ejpam-6178	61	14	homomorphism	homomorphism	NOUN
ejpam-6178	61	15	,	,	PUNCT
ejpam-6178	61	16	(	(	PUNCT
ejpam-6178	61	17	x	x	NOUN
ejpam-6178	61	18	,	,	PUNCT
ejpam-6178	61	19	◦	◦	NOUN
ejpam-6178	61	20	,	,	PUNCT
ejpam-6178	61	21	1x	1x	NUM
ejpam-6178	61	22	)	)	PUNCT
ejpam-6178	61	23	,	,	PUNCT
ejpam-6178	61	24	(	(	PUNCT
ejpam-6178	61	25	y	y	NOUN
ejpam-6178	61	26	,	,	PUNCT
ejpam-6178	61	27	∗	∗	NOUN
ejpam-6178	61	28	,	,	PUNCT
ejpam-6178	61	29	1y	1y	NOUN
ejpam-6178	61	30	)	)	PUNCT
ejpam-6178	61	31	be	be	AUX
ejpam-6178	61	32	db	db	NOUN
ejpam-6178	61	33	-	-	PUNCT
ejpam-6178	61	34	algebras	algebras	X
ejpam-6178	61	35	,	,	PUNCT
ejpam-6178	61	36	then	then	ADV
ejpam-6178	61	37	φ	φ	PROPN
ejpam-6178	61	38	is	be	AUX
ejpam-6178	61	39	a	a	DET
ejpam-6178	61	40	db	db	NOUN
ejpam-6178	61	41	-	-	PUNCT
ejpam-6178	61	42	monomorphism	monomorphism	NOUN
ejpam-6178	61	43	if	if	SCONJ
ejpam-6178	61	44	and	and	CCONJ
ejpam-6178	61	45	only	only	ADV
ejpam-6178	61	46	if	if	SCONJ
ejpam-6178	61	47	kerφ	kerφ	PROPN
ejpam-6178	61	48	=	=	SYM
ejpam-6178	61	49	1x	1x	PROPN
ejpam-6178	61	50	.	.	PUNCT
ejpam-6178	62	1	theorem	theorem	VERB
ejpam-6178	62	2	4	4	NUM
ejpam-6178	62	3	.	.	PUNCT
ejpam-6178	63	1	[	[	X
ejpam-6178	63	2	11	11	NUM
ejpam-6178	63	3	]	]	PUNCT
ejpam-6178	63	4	let	let	VERB
ejpam-6178	63	5	s	s	PRON
ejpam-6178	63	6	be	be	AUX
ejpam-6178	63	7	a	a	DET
ejpam-6178	63	8	normal	normal	ADJ
ejpam-6178	63	9	db	db	NOUN
ejpam-6178	63	10	-	-	PUNCT
ejpam-6178	63	11	subalgebra	subalgebra	NOUN
ejpam-6178	63	12	of	of	ADP
ejpam-6178	63	13	a	a	DET
ejpam-6178	63	14	db	db	NOUN
ejpam-6178	63	15	-	-	PUNCT
ejpam-6178	63	16	algebra	algebra	NOUN
ejpam-6178	63	17	(	(	PUNCT
ejpam-6178	63	18	x	x	X
ejpam-6178	63	19	,	,	PUNCT
ejpam-6178	63	20	◦	◦	NOUN
ejpam-6178	63	21	,	,	PUNCT
ejpam-6178	63	22	1	1	NUM
ejpam-6178	63	23	)	)	PUNCT
ejpam-6178	63	24	.	.	PUNCT
ejpam-6178	64	1	then	then	ADV
ejpam-6178	64	2	the	the	DET
ejpam-6178	64	3	mapping	mapping	NOUN
ejpam-6178	64	4	φ	φ	X
ejpam-6178	64	5	:	:	PUNCT
ejpam-6178	64	6	x	x	X
ejpam-6178	64	7	→	→	X
ejpam-6178	64	8	(	(	PUNCT
ejpam-6178	64	9	x	x	SYM
ejpam-6178	64	10	/	/	SYM
ejpam-6178	64	11	s	s	PROPN
ejpam-6178	64	12	,	,	PUNCT
ejpam-6178	64	13	∗	∗	NOUN
ejpam-6178	64	14	,	,	PUNCT
ejpam-6178	64	15	[	[	X
ejpam-6178	64	16	1]s	1]s	NOUN
ejpam-6178	64	17	)	)	PUNCT
ejpam-6178	64	18	given	give	VERB
ejpam-6178	64	19	by	by	ADP
ejpam-6178	64	20	φ(x	φ(x	NOUN
ejpam-6178	64	21	)	)	PUNCT
ejpam-6178	64	22	=	=	PUNCT
ejpam-6178	65	1	[	[	X
ejpam-6178	65	2	x]s	x]s	NOUN
ejpam-6178	65	3	for	for	ADP
ejpam-6178	65	4	all	all	DET
ejpam-6178	65	5	x	x	SYM
ejpam-6178	65	6	∈	∈	NOUN
ejpam-6178	65	7	x	x	X
ejpam-6178	65	8	is	be	AUX
ejpam-6178	65	9	a	a	DET
ejpam-6178	65	10	db	db	NOUN
ejpam-6178	65	11	-	-	PUNCT
ejpam-6178	65	12	epimorphism	epimorphism	NOUN
ejpam-6178	65	13	and	and	CCONJ
ejpam-6178	65	14	kerφ	kerφ	PROPN
ejpam-6178	65	15	=	=	PUNCT
ejpam-6178	66	1	s.	s.	PROPN
ejpam-6178	66	2	the	the	DET
ejpam-6178	66	3	mapping	mapping	NOUN
ejpam-6178	66	4	is	be	AUX
ejpam-6178	66	5	called	call	VERB
ejpam-6178	66	6	the	the	DET
ejpam-6178	66	7	natural	natural	ADJ
ejpam-6178	66	8	db	db	NOUN
ejpam-6178	66	9	-	-	PUNCT
ejpam-6178	66	10	homomorphism	homomorphism	NOUN
ejpam-6178	66	11	from	from	ADP
ejpam-6178	66	12	x	x	PRON
ejpam-6178	66	13	onto	onto	ADP
ejpam-6178	66	14	x	x	PROPN
ejpam-6178	66	15	/	/	SYM
ejpam-6178	66	16	s.	s.	PROPN
ejpam-6178	66	17	remark	remark	PROPN
ejpam-6178	66	18	1	1	NUM
ejpam-6178	66	19	.	.	PUNCT
ejpam-6178	67	1	[	[	X
ejpam-6178	67	2	11	11	NUM
ejpam-6178	67	3	]	]	PUNCT
ejpam-6178	67	4	let	let	VERB
ejpam-6178	67	5	φ	φ	PROPN
ejpam-6178	67	6	be	be	AUX
ejpam-6178	67	7	a	a	DET
ejpam-6178	67	8	db	db	NOUN
ejpam-6178	67	9	-	-	PUNCT
ejpam-6178	67	10	homomorphism	homomorphism	NOUN
ejpam-6178	67	11	from	from	ADP
ejpam-6178	67	12	(	(	PUNCT
ejpam-6178	67	13	x	x	NOUN
ejpam-6178	67	14	,	,	PUNCT
ejpam-6178	67	15	◦	◦	NOUN
ejpam-6178	67	16	,	,	PUNCT
ejpam-6178	67	17	1x	1x	NUM
ejpam-6178	67	18	)	)	PUNCT
ejpam-6178	67	19	into	into	ADP
ejpam-6178	67	20	(	(	PUNCT
ejpam-6178	67	21	y	y	PROPN
ejpam-6178	67	22	,	,	PUNCT
ejpam-6178	67	23	∗	∗	NOUN
ejpam-6178	67	24	,	,	PUNCT
ejpam-6178	67	25	1y	1y	NOUN
ejpam-6178	67	26	)	)	PUNCT
ejpam-6178	67	27	.	.	PUNCT
ejpam-6178	68	1	if	if	SCONJ
ejpam-6178	68	2	φ	φ	PROPN
ejpam-6178	68	3	is	be	AUX
ejpam-6178	68	4	surjective	surjective	ADJ
ejpam-6178	68	5	,	,	PUNCT
ejpam-6178	68	6	then	then	ADV
ejpam-6178	68	7	(	(	PUNCT
ejpam-6178	68	8	x/	x/	PROPN
ejpam-6178	68	9	kerφ	kerφ	PROPN
ejpam-6178	68	10	,	,	PUNCT
ejpam-6178	68	11	θ	θ	PROPN
ejpam-6178	68	12	,	,	PUNCT
ejpam-6178	68	13	[	[	X
ejpam-6178	68	14	1]kerφ	1]kerφ	NUM
ejpam-6178	68	15	)	)	PUNCT
ejpam-6178	68	16	∼=	∼=	PROPN
ejpam-6178	68	17	y	y	NOUN
ejpam-6178	68	18	.	.	PUNCT
ejpam-6178	69	1	definition	definition	NOUN
ejpam-6178	69	2	6	6	NUM
ejpam-6178	69	3	.	.	PUNCT
ejpam-6178	70	1	[	[	X
ejpam-6178	70	2	18	18	NUM
ejpam-6178	70	3	]	]	PUNCT
ejpam-6178	70	4	let	let	VERB
ejpam-6178	70	5	x	x	PRON
ejpam-6178	70	6	be	be	AUX
ejpam-6178	70	7	a	a	DET
ejpam-6178	70	8	set	set	NOUN
ejpam-6178	70	9	.	.	PUNCT
ejpam-6178	71	1	a	a	DET
ejpam-6178	71	2	topology	topology	NOUN
ejpam-6178	71	3	(	(	PUNCT
ejpam-6178	71	4	or	or	CCONJ
ejpam-6178	71	5	topological	topological	ADJ
ejpam-6178	71	6	structure	structure	NOUN
ejpam-6178	71	7	)	)	PUNCT
ejpam-6178	71	8	in	in	ADP
ejpam-6178	71	9	x	x	PRON
ejpam-6178	71	10	is	be	AUX
ejpam-6178	71	11	a	a	DET
ejpam-6178	71	12	family	family	NOUN
ejpam-6178	71	13	τ	τ	PROPN
ejpam-6178	71	14	of	of	ADP
ejpam-6178	71	15	subsets	subset	NOUN
ejpam-6178	71	16	of	of	ADP
ejpam-6178	71	17	x	x	PRON
ejpam-6178	71	18	that	that	PRON
ejpam-6178	71	19	satisfies	satisfy	VERB
ejpam-6178	71	20	the	the	DET
ejpam-6178	71	21	following	following	NOUN
ejpam-6178	71	22	:	:	PUNCT
ejpam-6178	71	23	(	(	PUNCT
ejpam-6178	71	24	i	i	NOUN
ejpam-6178	71	25	)	)	PUNCT
ejpam-6178	71	26	x	x	PUNCT
ejpam-6178	71	27	and	and	CCONJ
ejpam-6178	71	28	∅	∅	NOUN
ejpam-6178	71	29	are	be	AUX
ejpam-6178	71	30	members	member	NOUN
ejpam-6178	71	31	of	of	ADP
ejpam-6178	71	32	τ	τ	PROPN
ejpam-6178	71	33	.	.	PUNCT
ejpam-6178	72	1	(	(	PUNCT
ejpam-6178	72	2	ii	ii	NOUN
ejpam-6178	72	3	)	)	PUNCT
ejpam-6178	72	4	each	each	DET
ejpam-6178	72	5	finite	finite	ADJ
ejpam-6178	72	6	intersection	intersection	NOUN
ejpam-6178	72	7	of	of	ADP
ejpam-6178	72	8	members	member	NOUN
ejpam-6178	72	9	of	of	ADP
ejpam-6178	72	10	τ	τ	PROPN
ejpam-6178	72	11	is	be	AUX
ejpam-6178	72	12	also	also	ADV
ejpam-6178	72	13	a	a	DET
ejpam-6178	72	14	member	member	NOUN
ejpam-6178	72	15	of	of	ADP
ejpam-6178	72	16	τ	τ	PROPN
ejpam-6178	72	17	.	.	PUNCT
ejpam-6178	73	1	(	(	PUNCT
ejpam-6178	73	2	iii	iii	X
ejpam-6178	73	3	)	)	PUNCT
ejpam-6178	73	4	each	each	DET
ejpam-6178	73	5	union	union	NOUN
ejpam-6178	73	6	of	of	ADP
ejpam-6178	73	7	members	member	NOUN
ejpam-6178	73	8	of	of	ADP
ejpam-6178	73	9	τ	τ	PROPN
ejpam-6178	73	10	is	be	AUX
ejpam-6178	73	11	also	also	ADV
ejpam-6178	73	12	a	a	DET
ejpam-6178	73	13	member	member	NOUN
ejpam-6178	73	14	of	of	ADP
ejpam-6178	73	15	τ	τ	PROPN
ejpam-6178	73	16	.	.	PUNCT
ejpam-6178	74	1	definition	definition	NOUN
ejpam-6178	74	2	7	7	NUM
ejpam-6178	74	3	.	.	PUNCT
ejpam-6178	75	1	[	[	X
ejpam-6178	75	2	18	18	NUM
ejpam-6178	75	3	]	]	PUNCT
ejpam-6178	75	4	a	a	DET
ejpam-6178	75	5	couple	couple	NOUN
ejpam-6178	75	6	(	(	PUNCT
ejpam-6178	75	7	x	x	NOUN
ejpam-6178	75	8	,	,	PUNCT
ejpam-6178	75	9	τ	τ	X
ejpam-6178	75	10	)	)	PUNCT
ejpam-6178	75	11	consisting	consist	VERB
ejpam-6178	75	12	of	of	ADP
ejpam-6178	75	13	a	a	DET
ejpam-6178	75	14	set	set	NOUN
ejpam-6178	75	15	x	x	PUNCT
ejpam-6178	75	16	and	and	CCONJ
ejpam-6178	75	17	a	a	DET
ejpam-6178	75	18	topology	topology	NOUN
ejpam-6178	75	19	τ	τ	PROPN
ejpam-6178	75	20	in	in	ADP
ejpam-6178	75	21	x	x	PROPN
ejpam-6178	75	22	is	be	AUX
ejpam-6178	75	23	called	call	VERB
ejpam-6178	75	24	a	a	DET
ejpam-6178	75	25	topological	topological	ADJ
ejpam-6178	75	26	space	space	NOUN
ejpam-6178	75	27	.	.	PUNCT
ejpam-6178	76	1	elements	element	NOUN
ejpam-6178	76	2	of	of	ADP
ejpam-6178	76	3	topological	topological	ADJ
ejpam-6178	76	4	spaces	space	NOUN
ejpam-6178	76	5	are	be	AUX
ejpam-6178	76	6	called	call	VERB
ejpam-6178	76	7	points	point	NOUN
ejpam-6178	76	8	.	.	PUNCT
ejpam-6178	77	1	the	the	DET
ejpam-6178	77	2	members	member	NOUN
ejpam-6178	77	3	of	of	ADP
ejpam-6178	77	4	τ	τ	PROPN
ejpam-6178	77	5	are	be	AUX
ejpam-6178	77	6	called	call	VERB
ejpam-6178	77	7	the	the	DET
ejpam-6178	77	8	open	open	ADJ
ejpam-6178	77	9	sets	set	NOUN
ejpam-6178	77	10	or	or	CCONJ
ejpam-6178	77	11	τ	τ	X
ejpam-6178	77	12	-open	-open	NOUN
ejpam-6178	77	13	sets	set	NOUN
ejpam-6178	77	14	of	of	ADP
ejpam-6178	77	15	the	the	DET
ejpam-6178	77	16	topological	topological	ADJ
ejpam-6178	77	17	space	space	NOUN
ejpam-6178	77	18	(	(	PUNCT
ejpam-6178	77	19	x	x	X
ejpam-6178	77	20	,	,	PUNCT
ejpam-6178	77	21	τ	τ	X
ejpam-6178	77	22	)	)	PUNCT
ejpam-6178	77	23	(	(	PUNCT
ejpam-6178	77	24	or	or	CCONJ
ejpam-6178	77	25	of	of	ADP
ejpam-6178	77	26	the	the	DET
ejpam-6178	77	27	topology	topology	NOUN
ejpam-6178	77	28	τ	τ	PROPN
ejpam-6178	77	29	)	)	PUNCT
ejpam-6178	77	30	.	.	PUNCT
ejpam-6178	78	1	r.	r.	PROPN
ejpam-6178	78	2	nuñez	nuñez	PROPN
ejpam-6178	78	3	,	,	PUNCT
ejpam-6178	78	4	k.	k.	PROPN
ejpam-6178	78	5	b.	b.	PROPN
ejpam-6178	78	6	fuentes	fuentes	PROPN
ejpam-6178	78	7	/	/	SYM
ejpam-6178	78	8	eur	eur	PROPN
ejpam-6178	78	9	.	.	PUNCT
ejpam-6178	79	1	j.	j.	PROPN
ejpam-6178	79	2	pure	pure	PROPN
ejpam-6178	79	3	appl	appl	PROPN
ejpam-6178	79	4	.	.	PROPN
ejpam-6178	79	5	math	math	PROPN
ejpam-6178	79	6	,	,	PUNCT
ejpam-6178	79	7	18	18	NUM
ejpam-6178	79	8	(	(	PUNCT
ejpam-6178	79	9	4	4	NUM
ejpam-6178	79	10	)	)	PUNCT
ejpam-6178	79	11	(	(	PUNCT
ejpam-6178	79	12	2025	2025	NUM
ejpam-6178	79	13	)	)	PUNCT
ejpam-6178	79	14	,	,	PUNCT
ejpam-6178	79	15	6178	6178	NUM
ejpam-6178	79	16	4	4	NUM
ejpam-6178	79	17	of	of	ADP
ejpam-6178	79	18	15	15	NUM
ejpam-6178	79	19	theorem	theorem	NOUN
ejpam-6178	79	20	5	5	NUM
ejpam-6178	79	21	.	.	PUNCT
ejpam-6178	80	1	[	[	X
ejpam-6178	80	2	18	18	NUM
ejpam-6178	80	3	]	]	PUNCT
ejpam-6178	80	4	let	let	VERB
ejpam-6178	80	5	b	b	NOUN
ejpam-6178	80	6	⊆	⊆	NUM
ejpam-6178	80	7	τ	τ	X
ejpam-6178	80	8	be	be	AUX
ejpam-6178	80	9	a	a	DET
ejpam-6178	80	10	basis	basis	NOUN
ejpam-6178	80	11	for	for	ADP
ejpam-6178	80	12	τ	τ	PROPN
ejpam-6178	80	13	.	.	PUNCT
ejpam-6178	81	1	then	then	ADV
ejpam-6178	81	2	a	a	PRON
ejpam-6178	81	3	is	be	AUX
ejpam-6178	81	4	open	open	ADJ
ejpam-6178	81	5	if	if	SCONJ
ejpam-6178	81	6	and	and	CCONJ
ejpam-6178	81	7	only	only	ADV
ejpam-6178	81	8	if	if	SCONJ
ejpam-6178	81	9	for	for	ADP
ejpam-6178	81	10	each	each	DET
ejpam-6178	81	11	x	x	SYM
ejpam-6178	81	12	∈	∈	PROPN
ejpam-6178	81	13	a	a	PRON
ejpam-6178	81	14	,	,	PUNCT
ejpam-6178	81	15	there	there	PRON
ejpam-6178	81	16	exist	exist	VERB
ejpam-6178	81	17	a	a	DET
ejpam-6178	81	18	u	u	NOUN
ejpam-6178	81	19	in	in	ADP
ejpam-6178	81	20	b	b	NOUN
ejpam-6178	81	21	with	with	ADP
ejpam-6178	81	22	x	x	PROPN
ejpam-6178	81	23	∈	∈	PROPN
ejpam-6178	81	24	u	u	NOUN
ejpam-6178	81	25	⊆	⊆	NUM
ejpam-6178	81	26	a.	a.	NOUN
ejpam-6178	81	27	equivalently	equivalently	ADV
ejpam-6178	81	28	,	,	PUNCT
ejpam-6178	81	29	since	since	SCONJ
ejpam-6178	81	30	τ	τ	PROPN
ejpam-6178	81	31	is	be	AUX
ejpam-6178	81	32	a	a	DET
ejpam-6178	81	33	basis	basis	NOUN
ejpam-6178	81	34	for	for	ADP
ejpam-6178	81	35	itself	itself	PRON
ejpam-6178	81	36	,	,	PUNCT
ejpam-6178	81	37	then	then	ADV
ejpam-6178	81	38	a	a	PRON
ejpam-6178	81	39	is	be	AUX
ejpam-6178	81	40	open	open	ADJ
ejpam-6178	81	41	if	if	SCONJ
ejpam-6178	81	42	and	and	CCONJ
ejpam-6178	81	43	only	only	ADV
ejpam-6178	81	44	if	if	SCONJ
ejpam-6178	81	45	for	for	ADP
ejpam-6178	81	46	each	each	DET
ejpam-6178	81	47	x	x	SYM
ejpam-6178	81	48	∈	∈	PROPN
ejpam-6178	81	49	a	a	PRON
ejpam-6178	81	50	,	,	PUNCT
ejpam-6178	81	51	there	there	PRON
ejpam-6178	81	52	exist	exist	VERB
ejpam-6178	81	53	a	a	DET
ejpam-6178	81	54	u	u	NOUN
ejpam-6178	81	55	in	in	ADP
ejpam-6178	81	56	τ	τ	PROPN
ejpam-6178	81	57	with	with	ADP
ejpam-6178	81	58	x	x	PROPN
ejpam-6178	81	59	∈	∈	PROPN
ejpam-6178	81	60	u	u	NOUN
ejpam-6178	81	61	⊆	⊆	NUM
ejpam-6178	81	62	a.	a.	NOUN
ejpam-6178	81	63	definition	definition	NOUN
ejpam-6178	81	64	8	8	NUM
ejpam-6178	81	65	.	.	PUNCT
ejpam-6178	82	1	[	[	X
ejpam-6178	82	2	18	18	NUM
ejpam-6178	82	3	]	]	X
ejpam-6178	82	4	let	let	AUX
ejpam-6178	82	5	(	(	PUNCT
ejpam-6178	82	6	x	x	NOUN
ejpam-6178	82	7	,	,	PUNCT
ejpam-6178	82	8	τx	τx	ADJ
ejpam-6178	82	9	)	)	PUNCT
ejpam-6178	82	10	and	and	CCONJ
ejpam-6178	82	11	(	(	PUNCT
ejpam-6178	82	12	y	y	PROPN
ejpam-6178	82	13	,	,	PUNCT
ejpam-6178	82	14	τy	τy	PART
ejpam-6178	82	15	)	)	PUNCT
ejpam-6178	82	16	be	be	AUX
ejpam-6178	82	17	topological	topological	ADJ
ejpam-6178	82	18	spaces	space	NOUN
ejpam-6178	82	19	.	.	PUNCT
ejpam-6178	83	1	a	a	DET
ejpam-6178	83	2	map	map	NOUN
ejpam-6178	83	3	f	f	X
ejpam-6178	83	4	:	:	PUNCT
ejpam-6178	83	5	x	x	X
ejpam-6178	83	6	→	→	SYM
ejpam-6178	83	7	y	y	PROPN
ejpam-6178	83	8	is	be	AUX
ejpam-6178	83	9	called	call	VERB
ejpam-6178	83	10	continuous	continuous	ADJ
ejpam-6178	83	11	if	if	SCONJ
ejpam-6178	83	12	the	the	DET
ejpam-6178	83	13	inverse	inverse	ADJ
ejpam-6178	83	14	image	image	NOUN
ejpam-6178	83	15	of	of	ADP
ejpam-6178	83	16	each	each	DET
ejpam-6178	83	17	open	open	ADJ
ejpam-6178	83	18	set	set	NOUN
ejpam-6178	83	19	in	in	ADP
ejpam-6178	83	20	y	y	PROPN
ejpam-6178	83	21	is	be	AUX
ejpam-6178	83	22	open	open	ADJ
ejpam-6178	83	23	in	in	ADP
ejpam-6178	83	24	x	x	PROPN
ejpam-6178	83	25	(	(	PUNCT
ejpam-6178	83	26	that	that	PRON
ejpam-6178	83	27	is	is	ADV
ejpam-6178	83	28	,	,	PUNCT
ejpam-6178	83	29	if	if	SCONJ
ejpam-6178	83	30	f−1	f−1	PROPN
ejpam-6178	83	31	maps	map	VERB
ejpam-6178	83	32	τy	τy	NOUN
ejpam-6178	83	33	into	into	ADP
ejpam-6178	83	34	τx	τx	PROPN
ejpam-6178	83	35	)	)	PUNCT
ejpam-6178	83	36	.	.	PUNCT
ejpam-6178	84	1	a	a	DET
ejpam-6178	84	2	map	map	NOUN
ejpam-6178	84	3	sending	send	VERB
ejpam-6178	84	4	open	open	ADJ
ejpam-6178	84	5	sets	set	NOUN
ejpam-6178	84	6	to	to	PART
ejpam-6178	84	7	open	open	VERB
ejpam-6178	84	8	sets	set	NOUN
ejpam-6178	84	9	is	be	AUX
ejpam-6178	84	10	called	call	VERB
ejpam-6178	84	11	an	an	DET
ejpam-6178	84	12	open	open	ADJ
ejpam-6178	84	13	map	map	NOUN
ejpam-6178	84	14	.	.	PUNCT
ejpam-6178	85	1	theorem	theorem	VERB
ejpam-6178	85	2	6	6	NUM
ejpam-6178	85	3	.	.	PUNCT
ejpam-6178	86	1	[	[	X
ejpam-6178	86	2	18	18	NUM
ejpam-6178	86	3	]	]	PUNCT
ejpam-6178	86	4	let	let	VERB
ejpam-6178	86	5	x	x	PRON
ejpam-6178	86	6	and	and	CCONJ
ejpam-6178	86	7	y	y	PROPN
ejpam-6178	86	8	be	be	AUX
ejpam-6178	86	9	topological	topological	ADJ
ejpam-6178	86	10	space	space	NOUN
ejpam-6178	86	11	and	and	CCONJ
ejpam-6178	86	12	f	f	NOUN
ejpam-6178	86	13	:	:	PUNCT
ejpam-6178	86	14	x	x	X
ejpam-6178	86	15	→	→	SYM
ejpam-6178	86	16	y	y	PROPN
ejpam-6178	86	17	.	.	PUNCT
ejpam-6178	87	1	then	then	ADV
ejpam-6178	87	2	f	f	PROPN
ejpam-6178	87	3	is	be	AUX
ejpam-6178	87	4	open	open	ADJ
ejpam-6178	87	5	if	if	SCONJ
ejpam-6178	87	6	and	and	CCONJ
ejpam-6178	87	7	only	only	ADV
ejpam-6178	87	8	if	if	SCONJ
ejpam-6178	87	9	for	for	ADP
ejpam-6178	87	10	each	each	DET
ejpam-6178	87	11	x	x	SYM
ejpam-6178	87	12	∈	∈	PROPN
ejpam-6178	87	13	x	x	X
ejpam-6178	87	14	and	and	CCONJ
ejpam-6178	87	15	neighborhood	neighborhood	NOUN
ejpam-6178	87	16	u	u	NOUN
ejpam-6178	87	17	of	of	ADP
ejpam-6178	87	18	x	x	PRON
ejpam-6178	87	19	,	,	PUNCT
ejpam-6178	87	20	there	there	PRON
ejpam-6178	87	21	exists	exist	VERB
ejpam-6178	87	22	a	a	DET
ejpam-6178	87	23	neighborhood	neighborhood	NOUN
ejpam-6178	87	24	w	w	NOUN
ejpam-6178	87	25	of	of	ADP
ejpam-6178	87	26	f(x	f(x	PROPN
ejpam-6178	87	27	)	)	PUNCT
ejpam-6178	87	28	in	in	ADP
ejpam-6178	87	29	y	y	PRON
ejpam-6178	87	30	such	such	ADJ
ejpam-6178	87	31	that	that	SCONJ
ejpam-6178	87	32	w	w	PROPN
ejpam-6178	87	33	⊆	⊆	NUM
ejpam-6178	87	34	f(u	f(u	PROPN
ejpam-6178	87	35	)	)	PUNCT
ejpam-6178	87	36	.	.	PUNCT
ejpam-6178	88	1	theorem	theorem	VERB
ejpam-6178	88	2	7	7	NUM
ejpam-6178	88	3	.	.	PUNCT
ejpam-6178	89	1	[	[	X
ejpam-6178	89	2	18	18	NUM
ejpam-6178	89	3	]	]	PUNCT
ejpam-6178	89	4	let	let	VERB
ejpam-6178	89	5	x	x	PRON
ejpam-6178	89	6	and	and	CCONJ
ejpam-6178	89	7	y	y	PROPN
ejpam-6178	89	8	be	be	AUX
ejpam-6178	89	9	topological	topological	ADJ
ejpam-6178	89	10	space	space	NOUN
ejpam-6178	89	11	and	and	CCONJ
ejpam-6178	89	12	f	f	NOUN
ejpam-6178	89	13	:	:	PUNCT
ejpam-6178	89	14	x	x	X
ejpam-6178	89	15	→	→	SYM
ejpam-6178	89	16	y	y	PROPN
ejpam-6178	89	17	.	.	PUNCT
ejpam-6178	90	1	then	then	ADV
ejpam-6178	90	2	f	f	PROPN
ejpam-6178	90	3	is	be	AUX
ejpam-6178	90	4	continuous	continuous	ADJ
ejpam-6178	90	5	if	if	SCONJ
ejpam-6178	90	6	and	and	CCONJ
ejpam-6178	90	7	only	only	ADV
ejpam-6178	90	8	if	if	SCONJ
ejpam-6178	90	9	for	for	ADP
ejpam-6178	90	10	each	each	DET
ejpam-6178	90	11	x	x	SYM
ejpam-6178	90	12	∈	∈	PROPN
ejpam-6178	90	13	x	x	X
ejpam-6178	90	14	and	and	CCONJ
ejpam-6178	90	15	each	each	DET
ejpam-6178	90	16	neighborhood	neighborhood	NOUN
ejpam-6178	90	17	of	of	ADP
ejpam-6178	90	18	w	w	PROPN
ejpam-6178	90	19	of	of	ADP
ejpam-6178	90	20	f(x	f(x	PROPN
ejpam-6178	90	21	)	)	PUNCT
ejpam-6178	90	22	in	in	ADP
ejpam-6178	90	23	y	y	PROPN
ejpam-6178	90	24	,	,	PUNCT
ejpam-6178	90	25	there	there	PRON
ejpam-6178	90	26	exists	exist	VERB
ejpam-6178	90	27	a	a	DET
ejpam-6178	90	28	neighborhood	neighborhood	NOUN
ejpam-6178	90	29	v	v	NOUN
ejpam-6178	90	30	of	of	ADP
ejpam-6178	90	31	x	x	PUNCT
ejpam-6178	90	32	in	in	ADP
ejpam-6178	90	33	x	x	X
ejpam-6178	90	34	such	such	ADJ
ejpam-6178	90	35	that	that	SCONJ
ejpam-6178	90	36	f(v	f(v	PROPN
ejpam-6178	90	37	)	)	PUNCT
ejpam-6178	90	38	⊆	⊆	NUM
ejpam-6178	90	39	w	w	NOUN
ejpam-6178	90	40	.	.	PUNCT
ejpam-6178	91	1	definition	definition	NOUN
ejpam-6178	91	2	9	9	NUM
ejpam-6178	91	3	.	.	PUNCT
ejpam-6178	92	1	[	[	X
ejpam-6178	92	2	18	18	NUM
ejpam-6178	92	3	]	]	PUNCT
ejpam-6178	92	4	let	let	VERB
ejpam-6178	92	5	{	{	PUNCT
ejpam-6178	92	6	yα	yα	NOUN
ejpam-6178	93	1	|	|	ADV
ejpam-6178	93	2	i	i	PRON
ejpam-6178	93	3	∈	∈	VERB
ejpam-6178	93	4	a	a	DET
ejpam-6178	93	5	}	}	PUNCT
ejpam-6178	93	6	be	be	AUX
ejpam-6178	93	7	any	any	DET
ejpam-6178	93	8	family	family	NOUN
ejpam-6178	93	9	of	of	ADP
ejpam-6178	93	10	topological	topological	ADJ
ejpam-6178	93	11	spaces	space	NOUN
ejpam-6178	93	12	.	.	PUNCT
ejpam-6178	94	1	for	for	ADP
ejpam-6178	94	2	each	each	DET
ejpam-6178	94	3	α	α	NOUN
ejpam-6178	94	4	∈	∈	PROPN
ejpam-6178	94	5	a	a	PRON
ejpam-6178	94	6	,	,	PUNCT
ejpam-6178	94	7	let	let	VERB
ejpam-6178	94	8	τα	τα	PRON
ejpam-6178	94	9	the	the	DET
ejpam-6178	94	10	topology	topology	NOUN
ejpam-6178	94	11	for	for	ADP
ejpam-6178	94	12	yα	yα	NOUN
ejpam-6178	94	13	.	.	PUNCT
ejpam-6178	95	1	the	the	DET
ejpam-6178	95	2	cartersian	cartersian	ADJ
ejpam-6178	95	3	product	product	NOUN
ejpam-6178	95	4	topology	topology	NOUN
ejpam-6178	95	5	in	in	ADP
ejpam-6178	95	6	∏	∏	PROPN
ejpam-6178	95	7	α	α	PROPN
ejpam-6178	95	8	yα	yα	NOUN
ejpam-6178	95	9	is	be	AUX
ejpam-6178	95	10	that	that	SCONJ
ejpam-6178	95	11	having	have	VERB
ejpam-6178	95	12	for	for	ADP
ejpam-6178	95	13	subbasis	subbasis	NOUN
ejpam-6178	95	14	all	all	DET
ejpam-6178	95	15	sets	set	NOUN
ejpam-6178	95	16	⟨uβ⟩	⟨uβ⟩	NOUN
ejpam-6178	95	17	=	=	SYM
ejpam-6178	96	1	ρ−1	ρ−1	PROPN
ejpam-6178	96	2	β	β	X
ejpam-6178	96	3	(	(	PUNCT
ejpam-6178	96	4	uβ	uβ	PROPN
ejpam-6178	96	5	)	)	PUNCT
ejpam-6178	96	6	,	,	PUNCT
ejpam-6178	96	7	where	where	SCONJ
ejpam-6178	96	8	ρ	ρ	NOUN
ejpam-6178	96	9	:	:	PUNCT
ejpam-6178	96	10	∏	∏	PROPN
ejpam-6178	96	11	α	α	NOUN
ejpam-6178	96	12	yα	yα	NOUN
ejpam-6178	96	13	→	→	SYM
ejpam-6178	96	14	yα	yα	NOUN
ejpam-6178	96	15	,	,	PUNCT
ejpam-6178	96	16	uβ	uβ	PROPN
ejpam-6178	96	17	ranges	range	VERB
ejpam-6178	96	18	over	over	ADP
ejpam-6178	96	19	all	all	DET
ejpam-6178	96	20	members	member	NOUN
ejpam-6178	96	21	of	of	ADP
ejpam-6178	96	22	τβ	τβ	NOUN
ejpam-6178	96	23	and	and	CCONJ
ejpam-6178	96	24	β	β	X
ejpam-6178	96	25	over	over	ADP
ejpam-6178	96	26	all	all	DET
ejpam-6178	96	27	elements	element	NOUN
ejpam-6178	96	28	of	of	ADP
ejpam-6178	96	29	a.	a.	NOUN
ejpam-6178	96	30	definition	definition	NOUN
ejpam-6178	96	31	10	10	NUM
ejpam-6178	96	32	.	.	PUNCT
ejpam-6178	97	1	[	[	X
ejpam-6178	97	2	10	10	NUM
ejpam-6178	97	3	]	]	PUNCT
ejpam-6178	97	4	let	let	VERB
ejpam-6178	97	5	x	x	PRON
ejpam-6178	97	6	be	be	AUX
ejpam-6178	97	7	a	a	DET
ejpam-6178	97	8	db	db	NOUN
ejpam-6178	97	9	-	-	PUNCT
ejpam-6178	97	10	algebra	algebra	NOUN
ejpam-6178	97	11	.	.	PUNCT
ejpam-6178	98	1	a	a	DET
ejpam-6178	98	2	topology	topology	NOUN
ejpam-6178	98	3	τ	τ	PROPN
ejpam-6178	98	4	on	on	ADP
ejpam-6178	98	5	x	x	PROPN
ejpam-6178	98	6	is	be	AUX
ejpam-6178	98	7	called	call	VERB
ejpam-6178	98	8	a	a	DET
ejpam-6178	98	9	dual	dual	ADJ
ejpam-6178	98	10	b	b	NOUN
ejpam-6178	98	11	-	-	NOUN
ejpam-6178	98	12	topology	topology	NOUN
ejpam-6178	98	13	and	and	CCONJ
ejpam-6178	98	14	the	the	DET
ejpam-6178	98	15	couple	couple	NOUN
ejpam-6178	98	16	(	(	PUNCT
ejpam-6178	98	17	x	x	NOUN
ejpam-6178	98	18	,	,	PUNCT
ejpam-6178	98	19	τ	τ	X
ejpam-6178	98	20	)	)	PUNCT
ejpam-6178	98	21	is	be	AUX
ejpam-6178	98	22	called	call	VERB
ejpam-6178	98	23	a	a	DET
ejpam-6178	98	24	dual	dual	ADJ
ejpam-6178	98	25	b	b	NOUN
ejpam-6178	98	26	-	-	PUNCT
ejpam-6178	98	27	topological	topological	ADJ
ejpam-6178	98	28	space	space	NOUN
ejpam-6178	98	29	.	.	PUNCT
ejpam-6178	99	1	remark	remark	PROPN
ejpam-6178	99	2	2	2	NUM
ejpam-6178	99	3	.	.	PUNCT
ejpam-6178	100	1	let	let	AUX
ejpam-6178	100	2	(	(	PUNCT
ejpam-6178	100	3	x	x	NOUN
ejpam-6178	100	4	,	,	PUNCT
ejpam-6178	100	5	τ	τ	X
ejpam-6178	100	6	)	)	PUNCT
ejpam-6178	100	7	be	be	AUX
ejpam-6178	100	8	a	a	DET
ejpam-6178	100	9	dual	dual	ADJ
ejpam-6178	100	10	b	b	NOUN
ejpam-6178	100	11	-	-	PUNCT
ejpam-6178	100	12	topological	topological	ADJ
ejpam-6178	100	13	space	space	NOUN
ejpam-6178	100	14	.	.	PUNCT
ejpam-6178	101	1	then	then	ADV
ejpam-6178	101	2	a	a	PRON
ejpam-6178	101	3	is	be	AUX
ejpam-6178	101	4	open	open	ADJ
ejpam-6178	101	5	if	if	SCONJ
ejpam-6178	101	6	and	and	CCONJ
ejpam-6178	101	7	only	only	ADV
ejpam-6178	101	8	if	if	SCONJ
ejpam-6178	101	9	for	for	ADP
ejpam-6178	101	10	each	each	DET
ejpam-6178	101	11	x	x	SYM
ejpam-6178	101	12	∈	∈	PROPN
ejpam-6178	101	13	a	a	PRON
ejpam-6178	101	14	,	,	PUNCT
ejpam-6178	101	15	there	there	PRON
ejpam-6178	101	16	exist	exist	VERB
ejpam-6178	101	17	a	a	DET
ejpam-6178	101	18	u	u	NOUN
ejpam-6178	101	19	∈	∈	PROPN
ejpam-6178	101	20	τ	τ	X
ejpam-6178	101	21	with	with	ADP
ejpam-6178	101	22	x	x	PROPN
ejpam-6178	101	23	∈	∈	PROPN
ejpam-6178	101	24	u	u	NOUN
ejpam-6178	101	25	⊆	⊆	NUM
ejpam-6178	101	26	a.	a.	NOUN
ejpam-6178	101	27	definition	definition	NOUN
ejpam-6178	101	28	11	11	NUM
ejpam-6178	101	29	.	.	PUNCT
ejpam-6178	102	1	[	[	X
ejpam-6178	102	2	10	10	NUM
ejpam-6178	102	3	]	]	X
ejpam-6178	102	4	the	the	DET
ejpam-6178	102	5	triple	triple	ADJ
ejpam-6178	102	6	(	(	PUNCT
ejpam-6178	102	7	x	x	NOUN
ejpam-6178	102	8	,	,	PUNCT
ejpam-6178	102	9	◦	◦	NOUN
ejpam-6178	102	10	,	,	PUNCT
ejpam-6178	102	11	τ	τ	X
ejpam-6178	102	12	)	)	PUNCT
ejpam-6178	102	13	is	be	AUX
ejpam-6178	102	14	called	call	VERB
ejpam-6178	102	15	a	a	DET
ejpam-6178	102	16	topological	topological	ADJ
ejpam-6178	102	17	dual	dual	ADJ
ejpam-6178	102	18	b	b	NOUN
ejpam-6178	102	19	-	-	PUNCT
ejpam-6178	102	20	algebra	algebra	NOUN
ejpam-6178	102	21	(	(	PUNCT
ejpam-6178	102	22	or	or	CCONJ
ejpam-6178	102	23	tdbalgebra	tdbalgebra	NOUN
ejpam-6178	102	24	)	)	PUNCT
ejpam-6178	102	25	if	if	SCONJ
ejpam-6178	102	26	τ	τ	PROPN
ejpam-6178	102	27	is	be	AUX
ejpam-6178	102	28	a	a	DET
ejpam-6178	102	29	dual	dual	ADJ
ejpam-6178	102	30	b	b	NOUN
ejpam-6178	102	31	-	-	NOUN
ejpam-6178	102	32	topology	topology	NOUN
ejpam-6178	102	33	and	and	CCONJ
ejpam-6178	102	34	the	the	DET
ejpam-6178	102	35	binary	binary	PROPN
ejpam-6178	102	36	operation	operation	NOUN
ejpam-6178	102	37	◦	◦	NOUN
ejpam-6178	102	38	:	:	PUNCT
ejpam-6178	102	39	x	x	X
ejpam-6178	102	40	×x	×x	ADP
ejpam-6178	102	41	→	→	SYM
ejpam-6178	102	42	x	x	X
ejpam-6178	102	43	is	be	AUX
ejpam-6178	102	44	continuous	continuous	ADJ
ejpam-6178	102	45	where	where	SCONJ
ejpam-6178	102	46	the	the	DET
ejpam-6178	102	47	topology	topology	NOUN
ejpam-6178	102	48	on	on	ADP
ejpam-6178	102	49	x	x	X
ejpam-6178	102	50	×x	×x	X
ejpam-6178	102	51	is	be	AUX
ejpam-6178	102	52	the	the	DET
ejpam-6178	102	53	cartesian	cartesian	ADJ
ejpam-6178	102	54	product	product	NOUN
ejpam-6178	102	55	topology	topology	NOUN
ejpam-6178	102	56	.	.	PUNCT
ejpam-6178	103	1	remark	remark	VERB
ejpam-6178	103	2	3	3	NUM
ejpam-6178	103	3	.	.	PUNCT
ejpam-6178	104	1	[	[	X
ejpam-6178	104	2	10	10	NUM
ejpam-6178	104	3	]	]	PUNCT
ejpam-6178	104	4	let	let	VERB
ejpam-6178	104	5	x	x	PRON
ejpam-6178	104	6	be	be	AUX
ejpam-6178	104	7	a	a	DET
ejpam-6178	104	8	db	db	NOUN
ejpam-6178	104	9	-	-	PUNCT
ejpam-6178	104	10	algebra	algebra	NOUN
ejpam-6178	104	11	and	and	CCONJ
ejpam-6178	104	12	nonempty	nonempty	X
ejpam-6178	104	13	a	a	DET
ejpam-6178	104	14	,	,	PUNCT
ejpam-6178	104	15	b	b	PROPN
ejpam-6178	104	16	⊆	⊆	NUM
ejpam-6178	104	17	x.	x.	NOUN
ejpam-6178	104	18	then	then	ADV
ejpam-6178	104	19	,	,	PUNCT
ejpam-6178	104	20	◦	◦	NOUN
ejpam-6178	104	21	(	(	PUNCT
ejpam-6178	104	22	a×b	a×b	PROPN
ejpam-6178	104	23	)	)	PUNCT
ejpam-6178	104	24	=	=	PUNCT
ejpam-6178	104	25	a	a	DET
ejpam-6178	104	26	◦	◦	NOUN
ejpam-6178	104	27	b	b	NOUN
ejpam-6178	104	28	where	where	SCONJ
ejpam-6178	104	29	a	a	DET
ejpam-6178	104	30	◦	◦	NOUN
ejpam-6178	104	31	b	b	NOUN
ejpam-6178	104	32	=	=	PUNCT
ejpam-6178	104	33	{	{	PUNCT
ejpam-6178	104	34	a	a	DET
ejpam-6178	104	35	◦	◦	NOUN
ejpam-6178	104	36	b	b	NOUN
ejpam-6178	104	37	|	|	ADV
ejpam-6178	104	38	a	a	DET
ejpam-6178	104	39	∈	∈	PROPN
ejpam-6178	104	40	a	a	PRON
ejpam-6178	104	41	,	,	PUNCT
ejpam-6178	104	42	b	b	PROPN
ejpam-6178	104	43	∈	∈	PROPN
ejpam-6178	104	44	b	b	NOUN
ejpam-6178	104	45	}	}	PUNCT
ejpam-6178	104	46	.	.	PUNCT
ejpam-6178	105	1	remark	remark	PROPN
ejpam-6178	105	2	4	4	NUM
ejpam-6178	105	3	.	.	PUNCT
ejpam-6178	106	1	let	let	VERB
ejpam-6178	106	2	x	x	PRON
ejpam-6178	106	3	be	be	AUX
ejpam-6178	106	4	a	a	DET
ejpam-6178	106	5	db	db	NOUN
ejpam-6178	106	6	-	-	PUNCT
ejpam-6178	106	7	algebra	algebra	NOUN
ejpam-6178	106	8	and	and	CCONJ
ejpam-6178	106	9	nonempty	nonempty	X
ejpam-6178	106	10	a	a	PRON
ejpam-6178	106	11	,	,	PUNCT
ejpam-6178	106	12	b	b	PROPN
ejpam-6178	106	13	⊆	⊆	NUM
ejpam-6178	106	14	x.	x.	NOUN
ejpam-6178	106	15	when	when	SCONJ
ejpam-6178	106	16	b	b	X
ejpam-6178	106	17	=	=	PRON
ejpam-6178	106	18	{	{	PUNCT
ejpam-6178	106	19	x	x	NOUN
ejpam-6178	106	20	}	}	PUNCT
ejpam-6178	106	21	,	,	PUNCT
ejpam-6178	106	22	then	then	ADV
ejpam-6178	106	23	a	a	DET
ejpam-6178	106	24	◦	◦	NOUN
ejpam-6178	106	25	{	{	PUNCT
ejpam-6178	106	26	x	x	NOUN
ejpam-6178	106	27	}	}	PUNCT
ejpam-6178	106	28	=	=	SYM
ejpam-6178	106	29	{	{	PUNCT
ejpam-6178	106	30	a	a	DET
ejpam-6178	106	31	◦	◦	NOUN
ejpam-6178	106	32	x	x	SYM
ejpam-6178	106	33	|	|	ADV
ejpam-6178	106	34	a	a	DET
ejpam-6178	106	35	∈	∈	NOUN
ejpam-6178	106	36	a	a	PRON
ejpam-6178	106	37	}	}	PUNCT
ejpam-6178	106	38	=	=	SYM
ejpam-6178	106	39	a	a	DET
ejpam-6178	106	40	◦	◦	NOUN
ejpam-6178	106	41	x.	x.	NOUN
ejpam-6178	106	42	theorem	theorem	VERB
ejpam-6178	106	43	8	8	NUM
ejpam-6178	106	44	.	.	PUNCT
ejpam-6178	107	1	[	[	X
ejpam-6178	107	2	10	10	NUM
ejpam-6178	107	3	]	]	PUNCT
ejpam-6178	107	4	let	let	VERB
ejpam-6178	107	5	x	x	PRON
ejpam-6178	107	6	be	be	AUX
ejpam-6178	107	7	a	a	DET
ejpam-6178	107	8	dual	dual	ADJ
ejpam-6178	107	9	b	b	NOUN
ejpam-6178	107	10	-	-	PUNCT
ejpam-6178	107	11	algebra	algebra	NOUN
ejpam-6178	107	12	and	and	CCONJ
ejpam-6178	107	13	τ	τ	PROPN
ejpam-6178	107	14	a	a	DET
ejpam-6178	107	15	dual	dual	ADJ
ejpam-6178	107	16	b	b	NOUN
ejpam-6178	107	17	-	-	NOUN
ejpam-6178	107	18	topology	topology	NOUN
ejpam-6178	107	19	.	.	PUNCT
ejpam-6178	108	1	then	then	ADV
ejpam-6178	108	2	(	(	PUNCT
ejpam-6178	108	3	x	x	X
ejpam-6178	108	4	,	,	PUNCT
ejpam-6178	108	5	◦	◦	NOUN
ejpam-6178	108	6	,	,	PUNCT
ejpam-6178	108	7	τ	τ	X
ejpam-6178	108	8	)	)	PUNCT
ejpam-6178	108	9	is	be	AUX
ejpam-6178	108	10	a	a	DET
ejpam-6178	108	11	tdb	tdb	NOUN
ejpam-6178	108	12	-	-	NOUN
ejpam-6178	108	13	algebra	algebra	NOUN
ejpam-6178	108	14	if	if	SCONJ
ejpam-6178	108	15	and	and	CCONJ
ejpam-6178	108	16	only	only	ADV
ejpam-6178	108	17	if	if	SCONJ
ejpam-6178	108	18	for	for	ADP
ejpam-6178	108	19	all	all	DET
ejpam-6178	108	20	x	x	NOUN
ejpam-6178	108	21	,	,	PUNCT
ejpam-6178	108	22	y	y	PROPN
ejpam-6178	108	23	∈	∈	PROPN
ejpam-6178	108	24	x	x	X
ejpam-6178	108	25	and	and	CCONJ
ejpam-6178	108	26	u(x	u(x	PROPN
ejpam-6178	108	27	◦	◦	NOUN
ejpam-6178	108	28	y	y	PROPN
ejpam-6178	108	29	)	)	PUNCT
ejpam-6178	108	30	,	,	PUNCT
ejpam-6178	108	31	there	there	PRON
ejpam-6178	108	32	exists	exist	VERB
ejpam-6178	108	33	u(x	u(x	NOUN
ejpam-6178	108	34	)	)	PUNCT
ejpam-6178	108	35	and	and	CCONJ
ejpam-6178	108	36	u(y	u(y	NOUN
ejpam-6178	108	37	)	)	PUNCT
ejpam-6178	108	38	such	such	ADJ
ejpam-6178	108	39	that	that	SCONJ
ejpam-6178	108	40	u(x	u(x	NOUN
ejpam-6178	108	41	)	)	PUNCT
ejpam-6178	108	42	◦	◦	NOUN
ejpam-6178	108	43	u(y	u(y	NOUN
ejpam-6178	108	44	)	)	PUNCT
ejpam-6178	108	45	⊆	⊆	NUM
ejpam-6178	108	46	u(x	u(x	PROPN
ejpam-6178	108	47	◦	◦	NOUN
ejpam-6178	108	48	y	y	NOUN
ejpam-6178	108	49	)	)	PUNCT
ejpam-6178	108	50	.	.	PUNCT
ejpam-6178	109	1	r.	r.	PROPN
ejpam-6178	109	2	nuñez	nuñez	PROPN
ejpam-6178	109	3	,	,	PUNCT
ejpam-6178	109	4	k.	k.	PROPN
ejpam-6178	109	5	b.	b.	PROPN
ejpam-6178	109	6	fuentes	fuentes	PROPN
ejpam-6178	109	7	/	/	SYM
ejpam-6178	109	8	eur	eur	PROPN
ejpam-6178	109	9	.	.	PUNCT
ejpam-6178	110	1	j.	j.	PROPN
ejpam-6178	110	2	pure	pure	PROPN
ejpam-6178	110	3	appl	appl	PROPN
ejpam-6178	110	4	.	.	PROPN
ejpam-6178	110	5	math	math	PROPN
ejpam-6178	110	6	,	,	PUNCT
ejpam-6178	110	7	18	18	NUM
ejpam-6178	110	8	(	(	PUNCT
ejpam-6178	110	9	4	4	NUM
ejpam-6178	110	10	)	)	PUNCT
ejpam-6178	110	11	(	(	PUNCT
ejpam-6178	110	12	2025	2025	NUM
ejpam-6178	110	13	)	)	PUNCT
ejpam-6178	110	14	,	,	PUNCT
ejpam-6178	110	15	6178	6178	NUM
ejpam-6178	110	16	5	5	NUM
ejpam-6178	110	17	of	of	ADP
ejpam-6178	110	18	15	15	NUM
ejpam-6178	110	19	example	example	NOUN
ejpam-6178	110	20	2	2	NUM
ejpam-6178	110	21	.	.	PUNCT
ejpam-6178	111	1	[	[	X
ejpam-6178	111	2	10	10	NUM
ejpam-6178	111	3	]	]	PUNCT
ejpam-6178	111	4	consider	consider	VERB
ejpam-6178	111	5	the	the	DET
ejpam-6178	111	6	the	the	DET
ejpam-6178	111	7	dual	dual	ADJ
ejpam-6178	111	8	b	b	NOUN
ejpam-6178	111	9	-	-	PUNCT
ejpam-6178	111	10	algebra	algebra	NOUN
ejpam-6178	111	11	x	x	X
ejpam-6178	111	12	=	=	SYM
ejpam-6178	111	13	{	{	PUNCT
ejpam-6178	111	14	1	1	NUM
ejpam-6178	111	15	,	,	PUNCT
ejpam-6178	111	16	a	a	DET
ejpam-6178	111	17	,	,	PUNCT
ejpam-6178	111	18	b	b	NOUN
ejpam-6178	111	19	,	,	PUNCT
ejpam-6178	111	20	c	c	NOUN
ejpam-6178	111	21	}	}	PUNCT
ejpam-6178	111	22	from	from	ADP
ejpam-6178	111	23	example	example	NOUN
ejpam-6178	111	24	1	1	NUM
ejpam-6178	111	25	and	and	CCONJ
ejpam-6178	111	26	let	let	VERB
ejpam-6178	111	27	τ	τ	PROPN
ejpam-6178	111	28	=	=	PRON
ejpam-6178	111	29	{	{	PUNCT
ejpam-6178	111	30	x,∅	x,∅	PROPN
ejpam-6178	111	31	,	,	PUNCT
ejpam-6178	111	32	{	{	PUNCT
ejpam-6178	111	33	1	1	NUM
ejpam-6178	111	34	,	,	PUNCT
ejpam-6178	111	35	a	a	PRON
ejpam-6178	111	36	}	}	PUNCT
ejpam-6178	111	37	,	,	PUNCT
ejpam-6178	111	38	{	{	PUNCT
ejpam-6178	111	39	b	b	X
ejpam-6178	111	40	,	,	PUNCT
ejpam-6178	111	41	c	c	NOUN
ejpam-6178	111	42	}	}	PUNCT
ejpam-6178	111	43	}	}	PUNCT
ejpam-6178	111	44	.	.	PUNCT
ejpam-6178	112	1	then	then	ADV
ejpam-6178	112	2	τ	τ	PROPN
ejpam-6178	112	3	is	be	AUX
ejpam-6178	112	4	a	a	DET
ejpam-6178	112	5	dual	dual	ADJ
ejpam-6178	112	6	b	b	NOUN
ejpam-6178	112	7	-	-	NOUN
ejpam-6178	112	8	topology	topology	NOUN
ejpam-6178	112	9	.	.	PUNCT
ejpam-6178	113	1	through	through	ADP
ejpam-6178	113	2	routine	routine	ADJ
ejpam-6178	113	3	calculations	calculation	NOUN
ejpam-6178	113	4	and	and	CCONJ
ejpam-6178	113	5	and	and	CCONJ
ejpam-6178	113	6	with	with	ADP
ejpam-6178	113	7	theorem	theorem	ADJ
ejpam-6178	113	8	8	8	NUM
ejpam-6178	113	9	,	,	PUNCT
ejpam-6178	113	10	(	(	PUNCT
ejpam-6178	113	11	x	x	X
ejpam-6178	113	12	,	,	PUNCT
ejpam-6178	113	13	◦	◦	NOUN
ejpam-6178	113	14	,	,	PUNCT
ejpam-6178	113	15	τ	τ	X
ejpam-6178	113	16	)	)	PUNCT
ejpam-6178	113	17	is	be	AUX
ejpam-6178	113	18	a	a	DET
ejpam-6178	113	19	tdb	tdb	NOUN
ejpam-6178	113	20	-	-	NOUN
ejpam-6178	113	21	algebra	algebra	NOUN
ejpam-6178	113	22	.	.	PUNCT
ejpam-6178	114	1	theorem	theorem	NOUN
ejpam-6178	114	2	9	9	NUM
ejpam-6178	114	3	.	.	PUNCT
ejpam-6178	115	1	[	[	X
ejpam-6178	115	2	19	19	NUM
ejpam-6178	115	3	]	]	X
ejpam-6178	115	4	let	let	VERB
ejpam-6178	115	5	f	f	PRON
ejpam-6178	115	6	:	:	PUNCT
ejpam-6178	115	7	x	x	X
ejpam-6178	115	8	→	→	SYM
ejpam-6178	115	9	y	y	X
ejpam-6178	115	10	be	be	AUX
ejpam-6178	115	11	a	a	DET
ejpam-6178	115	12	function	function	NOUN
ejpam-6178	115	13	and	and	CCONJ
ejpam-6178	115	14	let	let	VERB
ejpam-6178	115	15	a	a	DET
ejpam-6178	115	16	⊆	⊆	NUM
ejpam-6178	115	17	x	x	NOUN
ejpam-6178	115	18	and	and	CCONJ
ejpam-6178	115	19	c	c	PROPN
ejpam-6178	116	1	⊆	⊆	NUM
ejpam-6178	116	2	y	y	NOUN
ejpam-6178	116	3	.	.	PUNCT
ejpam-6178	117	1	then	then	ADV
ejpam-6178	117	2	(	(	PUNCT
ejpam-6178	117	3	i	i	NOUN
ejpam-6178	117	4	)	)	PUNCT
ejpam-6178	117	5	a	a	DET
ejpam-6178	117	6	⊆	⊆	NUM
ejpam-6178	117	7	f−1(f(a	f−1(f(a	NOUN
ejpam-6178	117	8	)	)	PUNCT
ejpam-6178	117	9	)	)	PUNCT
ejpam-6178	117	10	,	,	PUNCT
ejpam-6178	117	11	(	(	PUNCT
ejpam-6178	117	12	ii	ii	NOUN
ejpam-6178	117	13	)	)	PUNCT
ejpam-6178	117	14	f(f−1(b	f(f−1(b	PROPN
ejpam-6178	117	15	)	)	PUNCT
ejpam-6178	117	16	)	)	PUNCT
ejpam-6178	118	1	⊆	⊆	NUM
ejpam-6178	118	2	b	b	NOUN
ejpam-6178	118	3	,	,	PUNCT
ejpam-6178	118	4	(	(	PUNCT
ejpam-6178	118	5	iii	iii	NOUN
ejpam-6178	118	6	)	)	PUNCT
ejpam-6178	118	7	if	if	SCONJ
ejpam-6178	118	8	b	b	PROPN
ejpam-6178	118	9	⊆	⊆	NUM
ejpam-6178	118	10	c	c	X
ejpam-6178	118	11	,	,	PUNCT
ejpam-6178	118	12	f−1(b	f−1(b	PROPN
ejpam-6178	118	13	)	)	PUNCT
ejpam-6178	118	14	⊆	⊆	NUM
ejpam-6178	118	15	f−1(c	f−1(c	PROPN
ejpam-6178	118	16	)	)	PUNCT
ejpam-6178	118	17	.	.	PUNCT
ejpam-6178	119	1	theorem	theorem	VERB
ejpam-6178	119	2	10	10	NUM
ejpam-6178	119	3	.	.	PUNCT
ejpam-6178	120	1	[	[	X
ejpam-6178	120	2	19	19	NUM
ejpam-6178	120	3	]	]	X
ejpam-6178	120	4	let	let	VERB
ejpam-6178	120	5	f	f	PRON
ejpam-6178	120	6	:	:	PUNCT
ejpam-6178	120	7	x	x	X
ejpam-6178	120	8	→	→	SYM
ejpam-6178	120	9	y	y	X
ejpam-6178	120	10	be	be	AUX
ejpam-6178	120	11	a	a	DET
ejpam-6178	120	12	function	function	NOUN
ejpam-6178	120	13	and	and	CCONJ
ejpam-6178	120	14	let	let	VERB
ejpam-6178	120	15	{	{	PUNCT
ejpam-6178	120	16	ai	ai	VERB
ejpam-6178	120	17	|	|	ADV
ejpam-6178	121	1	i	i	PRON
ejpam-6178	121	2	∈	∈	PROPN
ejpam-6178	122	1	i	i	PRON
ejpam-6178	122	2	}	}	PUNCT
ejpam-6178	122	3	be	be	VERB
ejpam-6178	122	4	a	a	DET
ejpam-6178	122	5	collection	collection	NOUN
ejpam-6178	122	6	of	of	ADP
ejpam-6178	122	7	subsets	subset	NOUN
ejpam-6178	122	8	of	of	ADP
ejpam-6178	122	9	y	y	PROPN
ejpam-6178	122	10	.	.	PUNCT
ejpam-6178	123	1	then	then	ADV
ejpam-6178	123	2	(	(	PUNCT
ejpam-6178	123	3	i	i	NOUN
ejpam-6178	123	4	)	)	PUNCT
ejpam-6178	123	5	f−1(∪i∈i	f−1(∪i∈i	NOUN
ejpam-6178	123	6	ai	ai	VERB
ejpam-6178	123	7	)	)	PUNCT
ejpam-6178	123	8	=	=	PUNCT
ejpam-6178	123	9	∪i∈i	∪i∈i	PRON
ejpam-6178	123	10	f−1(ai	f−1(ai	NOUN
ejpam-6178	123	11	)	)	PUNCT
ejpam-6178	123	12	,	,	PUNCT
ejpam-6178	123	13	and	and	CCONJ
ejpam-6178	123	14	(	(	PUNCT
ejpam-6178	123	15	ii	ii	NOUN
ejpam-6178	123	16	)	)	PUNCT
ejpam-6178	123	17	f−1(∩i∈i	f−1(∩i∈i	NOUN
ejpam-6178	123	18	ai	ai	NOUN
ejpam-6178	123	19	)	)	PUNCT
ejpam-6178	123	20	=	=	SYM
ejpam-6178	123	21	∩i∈i	∩i∈i	ADJ
ejpam-6178	123	22	f−1(ai	f−1(ai	PROPN
ejpam-6178	123	23	)	)	PUNCT
ejpam-6178	123	24	.	.	PUNCT
ejpam-6178	124	1	3	3	X
ejpam-6178	124	2	.	.	X
ejpam-6178	124	3	results	result	NOUN
ejpam-6178	124	4	in	in	ADP
ejpam-6178	124	5	this	this	DET
ejpam-6178	124	6	section	section	NOUN
ejpam-6178	124	7	,	,	PUNCT
ejpam-6178	124	8	the	the	DET
ejpam-6178	124	9	topology	topology	NOUN
ejpam-6178	124	10	for	for	ADP
ejpam-6178	124	11	the	the	DET
ejpam-6178	124	12	quotient	quotient	NOUN
ejpam-6178	124	13	db	db	NOUN
ejpam-6178	124	14	-	-	PUNCT
ejpam-6178	124	15	algebra	algebra	NOUN
ejpam-6178	124	16	was	be	AUX
ejpam-6178	124	17	created	create	VERB
ejpam-6178	124	18	using	use	VERB
ejpam-6178	124	19	the	the	DET
ejpam-6178	124	20	natural	natural	ADJ
ejpam-6178	124	21	db	db	NOUN
ejpam-6178	124	22	-	-	PUNCT
ejpam-6178	124	23	homomorphism	homomorphism	NOUN
ejpam-6178	124	24	.	.	PUNCT
ejpam-6178	125	1	the	the	DET
ejpam-6178	125	2	researcher	researcher	NOUN
ejpam-6178	125	3	then	then	ADV
ejpam-6178	125	4	used	use	VERB
ejpam-6178	125	5	the	the	DET
ejpam-6178	125	6	natural	natural	ADJ
ejpam-6178	125	7	db	db	NOUN
ejpam-6178	125	8	-	-	PUNCT
ejpam-6178	125	9	homomorphism	homomorphism	NOUN
ejpam-6178	125	10	to	to	PART
ejpam-6178	125	11	determine	determine	VERB
ejpam-6178	125	12	some	some	DET
ejpam-6178	125	13	tdb	tdb	NOUN
ejpam-6178	125	14	-	-	PUNCT
ejpam-6178	125	15	homomorphisms	homomorphism	NOUN
ejpam-6178	125	16	.	.	PUNCT
ejpam-6178	126	1	furthermore	furthermore	ADV
ejpam-6178	126	2	,	,	PUNCT
ejpam-6178	126	3	the	the	DET
ejpam-6178	126	4	researcher	researcher	NOUN
ejpam-6178	126	5	established	establish	VERB
ejpam-6178	126	6	some	some	DET
ejpam-6178	126	7	tdbisomorphisms	tdbisomorphism	NOUN
ejpam-6178	126	8	.	.	PUNCT
ejpam-6178	127	1	the	the	DET
ejpam-6178	127	2	first	first	ADJ
ejpam-6178	127	3	theorem	theorem	NOUN
ejpam-6178	127	4	presented	present	VERB
ejpam-6178	127	5	a	a	DET
ejpam-6178	127	6	topology	topology	NOUN
ejpam-6178	127	7	for	for	ADP
ejpam-6178	127	8	a	a	DET
ejpam-6178	127	9	quotient	quotient	NOUN
ejpam-6178	127	10	db	db	NOUN
ejpam-6178	127	11	-	-	PUNCT
ejpam-6178	127	12	algebra	algebra	NOUN
ejpam-6178	127	13	.	.	PUNCT
ejpam-6178	128	1	note	note	VERB
ejpam-6178	128	2	that	that	SCONJ
ejpam-6178	128	3	a	a	DET
ejpam-6178	128	4	dbsubalgebra	dbsubalgebra	NOUN
ejpam-6178	128	5	s	s	X
ejpam-6178	128	6	of	of	ADP
ejpam-6178	128	7	x	x	PRON
ejpam-6178	128	8	should	should	AUX
ejpam-6178	128	9	be	be	AUX
ejpam-6178	128	10	normal	normal	ADJ
ejpam-6178	128	11	(	(	PUNCT
ejpam-6178	128	12	definition	definition	NOUN
ejpam-6178	128	13	3	3	NUM
ejpam-6178	128	14	)	)	PUNCT
ejpam-6178	128	15	to	to	PART
ejpam-6178	128	16	form	form	VERB
ejpam-6178	128	17	a	a	DET
ejpam-6178	128	18	congruence	congruence	NOUN
ejpam-6178	128	19	classes	class	NOUN
ejpam-6178	128	20	of	of	ADP
ejpam-6178	128	21	a	a	DET
ejpam-6178	128	22	dual	dual	ADJ
ejpam-6178	128	23	b	b	NOUN
ejpam-6178	128	24	-	-	PUNCT
ejpam-6178	128	25	algebra	algebra	NOUN
ejpam-6178	128	26	.	.	PUNCT
ejpam-6178	129	1	these	these	DET
ejpam-6178	129	2	congruence	congruence	PROPN
ejpam-6178	129	3	classes	class	NOUN
ejpam-6178	129	4	are	be	AUX
ejpam-6178	129	5	exactly	exactly	ADV
ejpam-6178	129	6	the	the	DET
ejpam-6178	129	7	elements	element	NOUN
ejpam-6178	129	8	of	of	ADP
ejpam-6178	129	9	the	the	DET
ejpam-6178	129	10	quotient	quotient	NOUN
ejpam-6178	129	11	db	db	NOUN
ejpam-6178	129	12	-	-	PUNCT
ejpam-6178	129	13	algebra	algebra	NOUN
ejpam-6178	129	14	and	and	CCONJ
ejpam-6178	129	15	were	be	AUX
ejpam-6178	129	16	used	use	VERB
ejpam-6178	129	17	to	to	PART
ejpam-6178	129	18	define	define	VERB
ejpam-6178	129	19	the	the	DET
ejpam-6178	129	20	natural	natural	ADJ
ejpam-6178	129	21	db	db	NOUN
ejpam-6178	129	22	-	-	PUNCT
ejpam-6178	129	23	homomorphism	homomorphism	NOUN
ejpam-6178	129	24	(	(	PUNCT
ejpam-6178	129	25	theorem	theorem	NOUN
ejpam-6178	129	26	4	4	NUM
ejpam-6178	129	27	)	)	PUNCT
ejpam-6178	129	28	.	.	PUNCT
ejpam-6178	130	1	these	these	DET
ejpam-6178	130	2	concepts	concept	NOUN
ejpam-6178	130	3	were	be	AUX
ejpam-6178	130	4	utilized	utilize	VERB
ejpam-6178	130	5	to	to	PART
ejpam-6178	130	6	obtain	obtain	VERB
ejpam-6178	130	7	the	the	DET
ejpam-6178	130	8	elements	element	NOUN
ejpam-6178	130	9	of	of	ADP
ejpam-6178	130	10	the	the	DET
ejpam-6178	130	11	topology	topology	NOUN
ejpam-6178	130	12	for	for	ADP
ejpam-6178	130	13	the	the	DET
ejpam-6178	130	14	quotient	quotient	NOUN
ejpam-6178	130	15	db	db	NOUN
ejpam-6178	130	16	-	-	PUNCT
ejpam-6178	130	17	algebra	algebra	NOUN
ejpam-6178	130	18	.	.	PUNCT
ejpam-6178	131	1	theorem	theorem	NOUN
ejpam-6178	131	2	11	11	NUM
ejpam-6178	131	3	.	.	PUNCT
ejpam-6178	132	1	let	let	VERB
ejpam-6178	132	2	s	s	PRON
ejpam-6178	132	3	be	be	AUX
ejpam-6178	132	4	a	a	DET
ejpam-6178	132	5	normal	normal	ADJ
ejpam-6178	132	6	db	db	NOUN
ejpam-6178	132	7	-	-	PUNCT
ejpam-6178	132	8	subalgebra	subalgebra	NOUN
ejpam-6178	132	9	of	of	ADP
ejpam-6178	132	10	a	a	DET
ejpam-6178	132	11	tdb	tdb	NOUN
ejpam-6178	132	12	-	-	NOUN
ejpam-6178	132	13	algebra	algebra	NOUN
ejpam-6178	132	14	(	(	PUNCT
ejpam-6178	132	15	x	x	X
ejpam-6178	132	16	,	,	PUNCT
ejpam-6178	132	17	◦	◦	NOUN
ejpam-6178	132	18	,	,	PUNCT
ejpam-6178	132	19	τ	τ	X
ejpam-6178	132	20	)	)	PUNCT
ejpam-6178	132	21	and	and	CCONJ
ejpam-6178	132	22	φ	φ	PROPN
ejpam-6178	132	23	is	be	AUX
ejpam-6178	132	24	a	a	DET
ejpam-6178	132	25	natural	natural	ADJ
ejpam-6178	132	26	db	db	NOUN
ejpam-6178	132	27	-	-	PUNCT
ejpam-6178	132	28	homomorphism	homomorphism	NOUN
ejpam-6178	132	29	from	from	ADP
ejpam-6178	132	30	x	x	PRON
ejpam-6178	132	31	to	to	ADP
ejpam-6178	132	32	x	x	PRON
ejpam-6178	132	33	/	/	SYM
ejpam-6178	132	34	s.	s.	PROPN
ejpam-6178	132	35	then	then	ADV
ejpam-6178	132	36	,	,	PUNCT
ejpam-6178	133	1	τs	τs	X
ejpam-6178	133	2	=	=	SYM
ejpam-6178	133	3	{	{	PUNCT
ejpam-6178	133	4	z	z	NOUN
ejpam-6178	133	5	⊆	⊆	NUM
ejpam-6178	133	6	x	x	SYM
ejpam-6178	133	7	/	/	SYM
ejpam-6178	133	8	s	s	PART
ejpam-6178	133	9	∣∣φ−1(z	∣∣φ−1(z	PROPN
ejpam-6178	133	10	)	)	PUNCT
ejpam-6178	133	11	∈	∈	PROPN
ejpam-6178	133	12	τ	τ	PROPN
ejpam-6178	133	13	}	}	PUNCT
ejpam-6178	133	14	is	be	AUX
ejpam-6178	133	15	a	a	DET
ejpam-6178	133	16	topology	topology	NOUN
ejpam-6178	133	17	on	on	ADP
ejpam-6178	133	18	x	x	PROPN
ejpam-6178	133	19	/	/	SYM
ejpam-6178	133	20	s.	s.	PROPN
ejpam-6178	133	21	furthermore	furthermore	ADV
ejpam-6178	133	22	,	,	PUNCT
ejpam-6178	133	23	φ	φ	PROPN
ejpam-6178	133	24	is	be	AUX
ejpam-6178	133	25	a	a	DET
ejpam-6178	133	26	continuous	continuous	ADJ
ejpam-6178	133	27	mapping	mapping	NOUN
ejpam-6178	133	28	.	.	PUNCT
ejpam-6178	134	1	proof	proof	NOUN
ejpam-6178	134	2	.	.	PUNCT
ejpam-6178	135	1	since	since	SCONJ
ejpam-6178	135	2	φ−1(∅	φ−1(∅	NOUN
ejpam-6178	135	3	)	)	PUNCT
ejpam-6178	135	4	=	=	SYM
ejpam-6178	135	5	∅	∅	NOUN
ejpam-6178	135	6	∈	∈	PROPN
ejpam-6178	135	7	τ	τ	X
ejpam-6178	135	8	,	,	PUNCT
ejpam-6178	135	9	it	it	PRON
ejpam-6178	135	10	implies	imply	VERB
ejpam-6178	135	11	that	that	SCONJ
ejpam-6178	135	12	∅	∅	NOUN
ejpam-6178	135	13	∈	∈	NOUN
ejpam-6178	135	14	τs	τ	NOUN
ejpam-6178	135	15	.	.	PUNCT
ejpam-6178	136	1	moreover	moreover	ADV
ejpam-6178	136	2	,	,	PUNCT
ejpam-6178	136	3	by	by	ADP
ejpam-6178	136	4	theorem	theorem	NOUN
ejpam-6178	136	5	4	4	NUM
ejpam-6178	136	6	,	,	PUNCT
ejpam-6178	136	7	φ	φ	PROPN
ejpam-6178	136	8	is	be	AUX
ejpam-6178	136	9	surjective	surjective	ADJ
ejpam-6178	136	10	which	which	PRON
ejpam-6178	136	11	implies	imply	VERB
ejpam-6178	136	12	that	that	SCONJ
ejpam-6178	136	13	φ(x	φ(x	NOUN
ejpam-6178	136	14	)	)	PUNCT
ejpam-6178	136	15	=	=	SYM
ejpam-6178	137	1	x	x	X
ejpam-6178	137	2	/	/	SYM
ejpam-6178	137	3	s.	s.	PROPN
ejpam-6178	137	4	hence	hence	ADV
ejpam-6178	137	5	,	,	PUNCT
ejpam-6178	137	6	by	by	ADP
ejpam-6178	137	7	theorem	theorem	NOUN
ejpam-6178	137	8	9	9	NUM
ejpam-6178	137	9	(	(	PUNCT
ejpam-6178	137	10	i	i	NOUN
ejpam-6178	137	11	)	)	PUNCT
ejpam-6178	137	12	,	,	PUNCT
ejpam-6178	137	13	x	x	X
ejpam-6178	137	14	⊆	⊆	NUM
ejpam-6178	137	15	φ−1(φ(x	φ−1(φ(x	NOUN
ejpam-6178	137	16	)	)	PUNCT
ejpam-6178	137	17	)	)	PUNCT
ejpam-6178	138	1	=	=	PUNCT
ejpam-6178	138	2	φ−1(x	φ−1(x	NOUN
ejpam-6178	138	3	/	/	SYM
ejpam-6178	138	4	s	s	NOUN
ejpam-6178	138	5	)	)	PUNCT
ejpam-6178	138	6	that	that	PRON
ejpam-6178	138	7	is	be	AUX
ejpam-6178	138	8	φ−1(x	φ−1(x	NOUN
ejpam-6178	138	9	/	/	SYM
ejpam-6178	138	10	s	s	NOUN
ejpam-6178	138	11	)	)	PUNCT
ejpam-6178	138	12	=	=	PUNCT
ejpam-6178	139	1	x	x	SYM
ejpam-6178	139	2	∈	∈	PROPN
ejpam-6178	139	3	τ	τ	X
ejpam-6178	139	4	.	.	PUNCT
ejpam-6178	140	1	then	then	ADV
ejpam-6178	140	2	x	x	X
ejpam-6178	140	3	/	/	SYM
ejpam-6178	140	4	s	s	PART
ejpam-6178	140	5	∈	∈	NOUN
ejpam-6178	140	6	τs	τ	NOUN
ejpam-6178	140	7	.	.	PUNCT
ejpam-6178	141	1	let	let	VERB
ejpam-6178	141	2	z1	z1	NOUN
ejpam-6178	141	3	,	,	PUNCT
ejpam-6178	141	4	z2	z2	PROPN
ejpam-6178	141	5	∈	∈	PROPN
ejpam-6178	141	6	τs	τs	X
ejpam-6178	141	7	.	.	PUNCT
ejpam-6178	142	1	then	then	ADV
ejpam-6178	142	2	φ−1(z1	φ−1(z1	NOUN
ejpam-6178	142	3	)	)	PUNCT
ejpam-6178	142	4	,	,	PUNCT
ejpam-6178	142	5	φ−1(z2	φ−1(z2	NOUN
ejpam-6178	142	6	)	)	PUNCT
ejpam-6178	142	7	∈	∈	PROPN
ejpam-6178	142	8	τ	τ	X
ejpam-6178	142	9	.	.	PUNCT
ejpam-6178	143	1	by	by	ADP
ejpam-6178	143	2	theorem	theorem	ADJ
ejpam-6178	143	3	10	10	NUM
ejpam-6178	143	4	(	(	PUNCT
ejpam-6178	143	5	ii	ii	NOUN
ejpam-6178	143	6	)	)	PUNCT
ejpam-6178	143	7	,	,	PUNCT
ejpam-6178	143	8	it	it	PRON
ejpam-6178	143	9	follows	follow	VERB
ejpam-6178	143	10	that	that	SCONJ
ejpam-6178	143	11	φ−1(z1	φ−1(z1	NOUN
ejpam-6178	143	12	∩z2	∩z2	PROPN
ejpam-6178	143	13	)	)	PUNCT
ejpam-6178	143	14	=	=	SYM
ejpam-6178	143	15	φ−1(z1)∩φ−1(z2	φ−1(z1)∩φ−1(z2	PROPN
ejpam-6178	143	16	)	)	PUNCT
ejpam-6178	143	17	∈	∈	PROPN
ejpam-6178	143	18	τ	τ	PROPN
ejpam-6178	143	19	.	.	PUNCT
ejpam-6178	144	1	hence	hence	ADV
ejpam-6178	144	2	,	,	PUNCT
ejpam-6178	144	3	z1	z1	PROPN
ejpam-6178	144	4	∩	∩	ADJ
ejpam-6178	144	5	z2	z2	PROPN
ejpam-6178	144	6	∈	∈	PROPN
ejpam-6178	144	7	τs	τs	X
ejpam-6178	144	8	.	.	PUNCT
ejpam-6178	145	1	let	let	VERB
ejpam-6178	145	2	{	{	PUNCT
ejpam-6178	145	3	zi|i	zi|i	NOUN
ejpam-6178	145	4	∈	∈	PROPN
ejpam-6178	146	1	i	i	PRON
ejpam-6178	146	2	}	}	PUNCT
ejpam-6178	146	3	be	be	VERB
ejpam-6178	146	4	any	any	DET
ejpam-6178	146	5	family	family	NOUN
ejpam-6178	146	6	of	of	ADP
ejpam-6178	146	7	elements	element	NOUN
ejpam-6178	146	8	in	in	ADP
ejpam-6178	146	9	τs	τs	X
ejpam-6178	146	10	.	.	PUNCT
ejpam-6178	147	1	then	then	ADV
ejpam-6178	147	2	φ−1(zi	φ−1(zi	NOUN
ejpam-6178	147	3	)	)	PUNCT
ejpam-6178	147	4	∈	∈	PROPN
ejpam-6178	147	5	τ	τ	X
ejpam-6178	147	6	,	,	PUNCT
ejpam-6178	147	7	∀i	∀i	X
ejpam-6178	147	8	∈	∈	PROPN
ejpam-6178	147	9	i.	i.	NOUN
ejpam-6178	147	10	by	by	ADP
ejpam-6178	147	11	theorem	theorem	NOUN
ejpam-6178	147	12	10	10	NUM
ejpam-6178	147	13	(	(	PUNCT
ejpam-6178	147	14	i	i	NOUN
ejpam-6178	147	15	)	)	PUNCT
ejpam-6178	147	16	,	,	PUNCT
ejpam-6178	147	17	φ−1(∪i∈i	φ−1(∪i∈i	ADJ
ejpam-6178	147	18	zi	zi	NOUN
ejpam-6178	147	19	)	)	PUNCT
ejpam-6178	147	20	=	=	PUNCT
ejpam-6178	147	21	∪i∈i	∪i∈i	PRON
ejpam-6178	147	22	φ−1(zi	φ−1(zi	PROPN
ejpam-6178	147	23	)	)	PUNCT
ejpam-6178	147	24	∈	∈	PROPN
ejpam-6178	147	25	τ	τ	PROPN
ejpam-6178	147	26	.	.	PUNCT
ejpam-6178	148	1	hence	hence	ADV
ejpam-6178	148	2	,	,	PUNCT
ejpam-6178	148	3	∪i∈i	∪i∈i	NUM
ejpam-6178	148	4	zi	zi	NOUN
ejpam-6178	148	5	∈	∈	PROPN
ejpam-6178	148	6	τs	τs	X
ejpam-6178	148	7	.	.	PUNCT
ejpam-6178	149	1	therefore	therefore	ADV
ejpam-6178	149	2	,	,	PUNCT
ejpam-6178	149	3	τs	τs	ADP
ejpam-6178	149	4	is	be	AUX
ejpam-6178	149	5	a	a	DET
ejpam-6178	149	6	topology	topology	NOUN
ejpam-6178	149	7	on	on	ADP
ejpam-6178	149	8	x	x	PROPN
ejpam-6178	149	9	/	/	SYM
ejpam-6178	149	10	s.	s.	PROPN
ejpam-6178	149	11	furthermore	furthermore	ADV
ejpam-6178	149	12	,	,	PUNCT
ejpam-6178	149	13	for	for	ADP
ejpam-6178	149	14	all	all	DET
ejpam-6178	149	15	o	o	NOUN
ejpam-6178	149	16	∈	∈	X
ejpam-6178	149	17	τs	τs	X
ejpam-6178	149	18	,	,	PUNCT
ejpam-6178	149	19	φ−1(o	φ−1(o	PROPN
ejpam-6178	149	20	)	)	PUNCT
ejpam-6178	149	21	∈	∈	PROPN
ejpam-6178	149	22	τ	τ	PROPN
ejpam-6178	149	23	which	which	PRON
ejpam-6178	149	24	implies	imply	VERB
ejpam-6178	149	25	that	that	SCONJ
ejpam-6178	149	26	φ	φ	PROPN
ejpam-6178	149	27	is	be	AUX
ejpam-6178	149	28	continuous	continuous	ADJ
ejpam-6178	149	29	.	.	PUNCT
ejpam-6178	150	1	the	the	DET
ejpam-6178	150	2	example	example	NOUN
ejpam-6178	150	3	3	3	NUM
ejpam-6178	150	4	illustrates	illustrate	NOUN
ejpam-6178	150	5	theorem	theorem	VERB
ejpam-6178	150	6	11	11	NUM
ejpam-6178	150	7	.	.	PUNCT
ejpam-6178	150	8	example	example	NOUN
ejpam-6178	151	1	3	3	X
ejpam-6178	151	2	.	.	X
ejpam-6178	151	3	consider	consider	VERB
ejpam-6178	151	4	the	the	DET
ejpam-6178	151	5	tdb	tdb	NOUN
ejpam-6178	151	6	-	-	NOUN
ejpam-6178	151	7	algebra	algebra	PROPN
ejpam-6178	151	8	(	(	PUNCT
ejpam-6178	151	9	x	x	X
ejpam-6178	151	10	,	,	PUNCT
ejpam-6178	151	11	◦	◦	NOUN
ejpam-6178	151	12	,	,	PUNCT
ejpam-6178	151	13	τ	τ	X
ejpam-6178	151	14	)	)	PUNCT
ejpam-6178	151	15	in	in	ADP
ejpam-6178	151	16	example	example	NOUN
ejpam-6178	151	17	2	2	NUM
ejpam-6178	151	18	.	.	X
ejpam-6178	151	19	note	note	VERB
ejpam-6178	151	20	that	that	SCONJ
ejpam-6178	151	21	s	s	VERB
ejpam-6178	151	22	=	=	X
ejpam-6178	151	23	{	{	PUNCT
ejpam-6178	151	24	1	1	NUM
ejpam-6178	151	25	}	}	PUNCT
ejpam-6178	151	26	is	be	AUX
ejpam-6178	151	27	a	a	DET
ejpam-6178	151	28	normal	normal	ADJ
ejpam-6178	151	29	db	db	NOUN
ejpam-6178	151	30	-	-	PUNCT
ejpam-6178	151	31	subalgebra	subalgebra	NOUN
ejpam-6178	151	32	of	of	ADP
ejpam-6178	151	33	x.	x.	NOUN
ejpam-6178	151	34	also	also	ADV
ejpam-6178	151	35	,	,	PUNCT
ejpam-6178	152	1	[	[	X
ejpam-6178	152	2	1]s	1]s	NUM
ejpam-6178	152	3	=	=	SYM
ejpam-6178	152	4	{	{	PUNCT
ejpam-6178	152	5	1	1	NUM
ejpam-6178	152	6	}	}	PUNCT
ejpam-6178	152	7	,	,	PUNCT
ejpam-6178	152	8	[	[	X
ejpam-6178	152	9	a]s	a]s	NOUN
ejpam-6178	152	10	=	=	SYM
ejpam-6178	152	11	{	{	PUNCT
ejpam-6178	152	12	a	a	NOUN
ejpam-6178	152	13	}	}	PUNCT
ejpam-6178	152	14	,	,	PUNCT
ejpam-6178	152	15	[	[	X
ejpam-6178	152	16	b]s	b]s	NOUN
ejpam-6178	152	17	=	=	PUNCT
ejpam-6178	152	18	{	{	PUNCT
ejpam-6178	152	19	b	b	NOUN
ejpam-6178	152	20	}	}	PUNCT
ejpam-6178	152	21	,	,	PUNCT
ejpam-6178	152	22	[	[	X
ejpam-6178	152	23	c]s	c]s	NOUN
ejpam-6178	152	24	=	=	SYM
ejpam-6178	152	25	{	{	PUNCT
ejpam-6178	152	26	c	c	NOUN
ejpam-6178	152	27	}	}	PUNCT
ejpam-6178	152	28	.	.	PUNCT
ejpam-6178	153	1	then	then	ADV
ejpam-6178	153	2	x	x	X
ejpam-6178	153	3	/	/	SYM
ejpam-6178	153	4	s	s	NOUN
ejpam-6178	153	5	=	=	PUNCT
ejpam-6178	153	6	{	{	PUNCT
ejpam-6178	153	7	{	{	PUNCT
ejpam-6178	153	8	1	1	NUM
ejpam-6178	153	9	}	}	PUNCT
ejpam-6178	153	10	,	,	PUNCT
ejpam-6178	153	11	{	{	PUNCT
ejpam-6178	153	12	a	a	X
ejpam-6178	153	13	}	}	PUNCT
ejpam-6178	153	14	,	,	PUNCT
ejpam-6178	153	15	{	{	PUNCT
ejpam-6178	153	16	b	b	NOUN
ejpam-6178	153	17	}	}	PUNCT
ejpam-6178	153	18	,	,	PUNCT
ejpam-6178	153	19	{	{	PUNCT
ejpam-6178	153	20	c	c	NOUN
ejpam-6178	153	21	}	}	PUNCT
ejpam-6178	153	22	}	}	PUNCT
ejpam-6178	153	23	.	.	PUNCT
ejpam-6178	154	1	hence	hence	ADV
ejpam-6178	154	2	,	,	PUNCT
ejpam-6178	154	3	τs	τs	X
ejpam-6178	154	4	=	=	SYM
ejpam-6178	154	5	{	{	PUNCT
ejpam-6178	154	6	x	x	X
ejpam-6178	154	7	/	/	SYM
ejpam-6178	154	8	s,∅	s,∅	NOUN
ejpam-6178	154	9	,	,	PUNCT
ejpam-6178	154	10	{	{	PUNCT
ejpam-6178	154	11	{	{	PUNCT
ejpam-6178	154	12	1	1	NUM
ejpam-6178	154	13	}	}	PUNCT
ejpam-6178	154	14	,	,	PUNCT
ejpam-6178	154	15	{	{	PUNCT
ejpam-6178	154	16	a	a	X
ejpam-6178	154	17	}	}	PUNCT
ejpam-6178	154	18	}	}	PUNCT
ejpam-6178	154	19	,	,	PUNCT
ejpam-6178	154	20	{	{	PUNCT
ejpam-6178	154	21	{	{	PUNCT
ejpam-6178	154	22	b	b	NOUN
ejpam-6178	154	23	}	}	PUNCT
ejpam-6178	154	24	,	,	PUNCT
ejpam-6178	154	25	{	{	PUNCT
ejpam-6178	154	26	c	c	NOUN
ejpam-6178	154	27	}	}	PUNCT
ejpam-6178	154	28	}	}	PUNCT
ejpam-6178	154	29	}	}	PUNCT
ejpam-6178	154	30	.	.	PUNCT
ejpam-6178	155	1	r.	r.	PROPN
ejpam-6178	155	2	nuñez	nuñez	PROPN
ejpam-6178	155	3	,	,	PUNCT
ejpam-6178	155	4	k.	k.	PROPN
ejpam-6178	155	5	b.	b.	PROPN
ejpam-6178	155	6	fuentes	fuentes	PROPN
ejpam-6178	155	7	/	/	SYM
ejpam-6178	155	8	eur	eur	PROPN
ejpam-6178	155	9	.	.	PUNCT
ejpam-6178	156	1	j.	j.	PROPN
ejpam-6178	156	2	pure	pure	PROPN
ejpam-6178	156	3	appl	appl	PROPN
ejpam-6178	156	4	.	.	PROPN
ejpam-6178	156	5	math	math	PROPN
ejpam-6178	156	6	,	,	PUNCT
ejpam-6178	156	7	18	18	NUM
ejpam-6178	156	8	(	(	PUNCT
ejpam-6178	156	9	4	4	NUM
ejpam-6178	156	10	)	)	PUNCT
ejpam-6178	156	11	(	(	PUNCT
ejpam-6178	156	12	2025	2025	NUM
ejpam-6178	156	13	)	)	PUNCT
ejpam-6178	156	14	,	,	PUNCT
ejpam-6178	156	15	6178	6178	NUM
ejpam-6178	156	16	6	6	NUM
ejpam-6178	156	17	of	of	ADP
ejpam-6178	156	18	15	15	NUM
ejpam-6178	156	19	by	by	ADP
ejpam-6178	156	20	definition	definition	NOUN
ejpam-6178	156	21	11	11	NUM
ejpam-6178	156	22	,	,	PUNCT
ejpam-6178	156	23	(	(	PUNCT
ejpam-6178	156	24	x	x	X
ejpam-6178	156	25	/	/	SYM
ejpam-6178	156	26	s	s	PROPN
ejpam-6178	156	27	,	,	PUNCT
ejpam-6178	156	28	∗	∗	NOUN
ejpam-6178	156	29	,	,	PUNCT
ejpam-6178	156	30	τs	τs	NOUN
ejpam-6178	156	31	)	)	PUNCT
ejpam-6178	156	32	is	be	AUX
ejpam-6178	156	33	a	a	DET
ejpam-6178	156	34	tdb	tdb	NOUN
ejpam-6178	156	35	-	-	NOUN
ejpam-6178	156	36	algebra	algebra	PROPN
ejpam-6178	156	37	(	(	PUNCT
ejpam-6178	156	38	see	see	VERB
ejpam-6178	156	39	appendix	appendix	NOUN
ejpam-6178	156	40	for	for	ADP
ejpam-6178	156	41	the	the	DET
ejpam-6178	156	42	manual	manual	ADJ
ejpam-6178	156	43	verification	verification	NOUN
ejpam-6178	156	44	)	)	PUNCT
ejpam-6178	156	45	.	.	PUNCT
ejpam-6178	157	1	in	in	ADP
ejpam-6178	157	2	general	general	ADJ
ejpam-6178	157	3	,	,	PUNCT
ejpam-6178	157	4	it	it	PRON
ejpam-6178	157	5	does	do	AUX
ejpam-6178	157	6	not	not	PART
ejpam-6178	157	7	necessarily	necessarily	ADV
ejpam-6178	157	8	imply	imply	VERB
ejpam-6178	157	9	that	that	SCONJ
ejpam-6178	157	10	if	if	SCONJ
ejpam-6178	157	11	s	s	NOUN
ejpam-6178	157	12	is	be	AUX
ejpam-6178	157	13	a	a	DET
ejpam-6178	157	14	normal	normal	ADJ
ejpam-6178	157	15	db	db	NOUN
ejpam-6178	157	16	-	-	PUNCT
ejpam-6178	157	17	subalgebra	subalgebra	NOUN
ejpam-6178	157	18	,	,	PUNCT
ejpam-6178	157	19	(	(	PUNCT
ejpam-6178	157	20	x	x	X
ejpam-6178	157	21	/	/	SYM
ejpam-6178	157	22	s	s	PROPN
ejpam-6178	157	23	,	,	PUNCT
ejpam-6178	157	24	∗	∗	NOUN
ejpam-6178	157	25	,	,	PUNCT
ejpam-6178	157	26	τs	τs	NOUN
ejpam-6178	157	27	)	)	PUNCT
ejpam-6178	157	28	is	be	AUX
ejpam-6178	157	29	a	a	DET
ejpam-6178	157	30	tdb	tdb	NOUN
ejpam-6178	157	31	-	-	NOUN
ejpam-6178	157	32	algebra	algebra	NOUN
ejpam-6178	157	33	.	.	PUNCT
ejpam-6178	158	1	notice	notice	VERB
ejpam-6178	158	2	that	that	SCONJ
ejpam-6178	158	3	in	in	ADP
ejpam-6178	158	4	example	example	NOUN
ejpam-6178	158	5	3	3	NUM
ejpam-6178	158	6	,	,	PUNCT
ejpam-6178	158	7	the	the	DET
ejpam-6178	158	8	image	image	NOUN
ejpam-6178	158	9	of	of	ADP
ejpam-6178	158	10	each	each	DET
ejpam-6178	158	11	open	open	ADJ
ejpam-6178	158	12	set	set	NOUN
ejpam-6178	158	13	in	in	ADP
ejpam-6178	158	14	x	x	PUNCT
ejpam-6178	158	15	is	be	AUX
ejpam-6178	158	16	open	open	ADJ
ejpam-6178	158	17	in	in	ADP
ejpam-6178	158	18	x	x	PROPN
ejpam-6178	158	19	/	/	SYM
ejpam-6178	158	20	s.	s.	PROPN
ejpam-6178	158	21	thus	thus	ADV
ejpam-6178	158	22	the	the	DET
ejpam-6178	158	23	mapping	mapping	NOUN
ejpam-6178	158	24	is	be	AUX
ejpam-6178	158	25	open	open	ADJ
ejpam-6178	158	26	.	.	PUNCT
ejpam-6178	159	1	hence	hence	ADV
ejpam-6178	159	2	,	,	PUNCT
ejpam-6178	159	3	the	the	DET
ejpam-6178	159	4	significance	significance	NOUN
ejpam-6178	159	5	of	of	ADP
ejpam-6178	159	6	the	the	DET
ejpam-6178	159	7	quotient	quotient	NOUN
ejpam-6178	159	8	topology	topology	NOUN
ejpam-6178	159	9	gives	give	VERB
ejpam-6178	159	10	another	another	DET
ejpam-6178	159	11	way	way	NOUN
ejpam-6178	159	12	in	in	ADP
ejpam-6178	159	13	determining	determine	VERB
ejpam-6178	159	14	tdb	tdb	PROPN
ejpam-6178	159	15	-	-	PUNCT
ejpam-6178	159	16	algebras	algebras	PROPN
ejpam-6178	159	17	.	.	PUNCT
ejpam-6178	160	1	that	that	PRON
ejpam-6178	160	2	is	be	AUX
ejpam-6178	160	3	,	,	PUNCT
ejpam-6178	160	4	to	to	PART
ejpam-6178	160	5	look	look	VERB
ejpam-6178	160	6	for	for	ADP
ejpam-6178	160	7	open	open	ADJ
ejpam-6178	160	8	maps	map	NOUN
ejpam-6178	160	9	between	between	ADP
ejpam-6178	160	10	a	a	DET
ejpam-6178	160	11	tdb	tdb	NOUN
ejpam-6178	160	12	-	-	NOUN
ejpam-6178	160	13	algebra	algebra	NOUN
ejpam-6178	160	14	x	x	PUNCT
ejpam-6178	160	15	with	with	ADP
ejpam-6178	160	16	its	its	PRON
ejpam-6178	160	17	corresponding	corresponding	ADJ
ejpam-6178	160	18	quotient	quotient	NOUN
ejpam-6178	160	19	dual	dual	ADJ
ejpam-6178	160	20	b	b	NOUN
ejpam-6178	160	21	-	-	PUNCT
ejpam-6178	160	22	algebra	algebra	NOUN
ejpam-6178	160	23	.	.	PUNCT
ejpam-6178	161	1	if	if	SCONJ
ejpam-6178	161	2	such	such	ADJ
ejpam-6178	161	3	map	map	NOUN
ejpam-6178	161	4	exists	exist	VERB
ejpam-6178	161	5	,	,	PUNCT
ejpam-6178	161	6	the	the	DET
ejpam-6178	161	7	quotient	quotient	NOUN
ejpam-6178	161	8	topology	topology	NOUN
ejpam-6178	161	9	makes	make	VERB
ejpam-6178	161	10	the	the	DET
ejpam-6178	161	11	binary	binary	ADJ
ejpam-6178	161	12	operation	operation	NOUN
ejpam-6178	161	13	defined	define	VERB
ejpam-6178	161	14	in	in	ADP
ejpam-6178	161	15	the	the	DET
ejpam-6178	161	16	quotient	quotient	NOUN
ejpam-6178	161	17	dual	dual	ADJ
ejpam-6178	161	18	balgebra	balgebra	VERB
ejpam-6178	161	19	continuous	continuous	ADJ
ejpam-6178	161	20	which	which	PRON
ejpam-6178	161	21	means	mean	VERB
ejpam-6178	161	22	that	that	SCONJ
ejpam-6178	161	23	it	it	PRON
ejpam-6178	161	24	is	be	AUX
ejpam-6178	161	25	always	always	ADV
ejpam-6178	161	26	guaranteed	guarantee	VERB
ejpam-6178	161	27	that	that	SCONJ
ejpam-6178	161	28	the	the	DET
ejpam-6178	161	29	inverse	inverse	ADJ
ejpam-6178	161	30	image	image	NOUN
ejpam-6178	161	31	of	of	ADP
ejpam-6178	161	32	each	each	DET
ejpam-6178	161	33	open	open	ADJ
ejpam-6178	161	34	set	set	NOUN
ejpam-6178	161	35	in	in	ADP
ejpam-6178	161	36	the	the	DET
ejpam-6178	161	37	quotient	quotient	NOUN
ejpam-6178	161	38	topology	topology	NOUN
ejpam-6178	161	39	is	be	AUX
ejpam-6178	161	40	open	open	ADJ
ejpam-6178	161	41	in	in	ADP
ejpam-6178	161	42	the	the	DET
ejpam-6178	161	43	topology	topology	NOUN
ejpam-6178	161	44	on	on	ADP
ejpam-6178	161	45	x	x	SYM
ejpam-6178	161	46	/	/	SYM
ejpam-6178	161	47	s	s	PART
ejpam-6178	161	48	×x	×x	X
ejpam-6178	161	49	/	/	SYM
ejpam-6178	161	50	s.	s.	PROPN
ejpam-6178	161	51	the	the	DET
ejpam-6178	161	52	next	next	ADJ
ejpam-6178	161	53	theorem	theorem	ADJ
ejpam-6178	161	54	summarizes	summarize	NOUN
ejpam-6178	161	55	this	this	DET
ejpam-6178	161	56	discussion	discussion	NOUN
ejpam-6178	161	57	.	.	PUNCT
ejpam-6178	162	1	theorem	theorem	NOUN
ejpam-6178	162	2	12	12	NUM
ejpam-6178	162	3	.	.	PUNCT
ejpam-6178	163	1	let	let	VERB
ejpam-6178	163	2	(	(	PUNCT
ejpam-6178	163	3	x	x	NOUN
ejpam-6178	163	4	,	,	PUNCT
ejpam-6178	163	5	◦	◦	NOUN
ejpam-6178	163	6	,	,	PUNCT
ejpam-6178	163	7	τ	τ	X
ejpam-6178	163	8	)	)	PUNCT
ejpam-6178	163	9	be	be	VERB
ejpam-6178	163	10	a	a	DET
ejpam-6178	163	11	tdb	tdb	NOUN
ejpam-6178	163	12	-	-	NOUN
ejpam-6178	163	13	algebra	algebra	PROPN
ejpam-6178	163	14	and	and	CCONJ
ejpam-6178	163	15	s	s	NOUN
ejpam-6178	163	16	⊆	⊆	NUM
ejpam-6178	163	17	x.	x.	NOUN
ejpam-6178	163	18	if	if	SCONJ
ejpam-6178	163	19	the	the	DET
ejpam-6178	163	20	natural	natural	ADJ
ejpam-6178	163	21	db	db	NOUN
ejpam-6178	163	22	-	-	PUNCT
ejpam-6178	163	23	homomorphism	homomorphism	NOUN
ejpam-6178	163	24	φ	φ	X
ejpam-6178	163	25	:	:	PUNCT
ejpam-6178	163	26	x	x	X
ejpam-6178	163	27	→	→	SYM
ejpam-6178	163	28	x	x	X
ejpam-6178	163	29	/	/	SYM
ejpam-6178	163	30	s	s	PART
ejpam-6178	163	31	is	be	AUX
ejpam-6178	163	32	an	an	DET
ejpam-6178	163	33	open	open	ADJ
ejpam-6178	163	34	map	map	NOUN
ejpam-6178	163	35	,	,	PUNCT
ejpam-6178	163	36	then	then	ADV
ejpam-6178	163	37	(	(	PUNCT
ejpam-6178	163	38	x	x	X
ejpam-6178	163	39	/	/	SYM
ejpam-6178	163	40	s	s	PROPN
ejpam-6178	163	41	,	,	PUNCT
ejpam-6178	163	42	∗	∗	NOUN
ejpam-6178	163	43	,	,	PUNCT
ejpam-6178	163	44	τs	τs	NOUN
ejpam-6178	163	45	)	)	PUNCT
ejpam-6178	163	46	is	be	AUX
ejpam-6178	163	47	a	a	DET
ejpam-6178	163	48	tdb	tdb	NOUN
ejpam-6178	163	49	-	-	NOUN
ejpam-6178	163	50	algebra	algebra	NOUN
ejpam-6178	163	51	.	.	PUNCT
ejpam-6178	164	1	proof	proof	NOUN
ejpam-6178	164	2	.	.	PUNCT
ejpam-6178	165	1	suppose	suppose	VERB
ejpam-6178	165	2	φ	φ	PROPN
ejpam-6178	165	3	is	be	AUX
ejpam-6178	165	4	open	open	ADJ
ejpam-6178	165	5	.	.	PUNCT
ejpam-6178	166	1	let	let	VERB
ejpam-6178	166	2	[	[	X
ejpam-6178	166	3	a]s	a]s	ADJ
ejpam-6178	166	4	,	,	PUNCT
ejpam-6178	167	1	[	[	X
ejpam-6178	167	2	b]s	b]s	NOUN
ejpam-6178	167	3	∈	∈	PROPN
ejpam-6178	167	4	x	x	PROPN
ejpam-6178	167	5	/	/	SYM
ejpam-6178	167	6	s	s	X
ejpam-6178	167	7	and	and	CCONJ
ejpam-6178	167	8	w	w	AUX
ejpam-6178	167	9	be	be	AUX
ejpam-6178	167	10	a	a	DET
ejpam-6178	167	11	neighborhood	neighborhood	NOUN
ejpam-6178	167	12	of	of	ADP
ejpam-6178	167	13	[	[	X
ejpam-6178	167	14	a]s	a]s	ADJ
ejpam-6178	167	15	∗	∗	NOUN
ejpam-6178	168	1	[	[	X
ejpam-6178	168	2	b]s	b]s	NOUN
ejpam-6178	168	3	.	.	PUNCT
ejpam-6178	169	1	then	then	ADV
ejpam-6178	169	2	φ−1(w	φ−1(w	ADJ
ejpam-6178	169	3	)	)	PUNCT
ejpam-6178	169	4	∈	∈	PROPN
ejpam-6178	169	5	τ	τ	PROPN
ejpam-6178	169	6	since	since	SCONJ
ejpam-6178	169	7	φ	φ	PROPN
ejpam-6178	169	8	is	be	AUX
ejpam-6178	169	9	a	a	DET
ejpam-6178	169	10	continuous	continuous	ADJ
ejpam-6178	169	11	mapping	mapping	NOUN
ejpam-6178	169	12	by	by	ADP
ejpam-6178	169	13	theorem	theorem	NOUN
ejpam-6178	169	14	11	11	NUM
ejpam-6178	169	15	.	.	PUNCT
ejpam-6178	170	1	note	note	VERB
ejpam-6178	170	2	that	that	SCONJ
ejpam-6178	170	3	φ(a	φ(a	ADJ
ejpam-6178	170	4	◦	◦	NOUN
ejpam-6178	170	5	b	b	NOUN
ejpam-6178	170	6	)	)	PUNCT
ejpam-6178	170	7	=	=	NOUN
ejpam-6178	171	1	[	[	X
ejpam-6178	171	2	a	a	DET
ejpam-6178	171	3	◦	◦	NOUN
ejpam-6178	171	4	b]s	b]s	NOUN
ejpam-6178	171	5	=	=	PUNCT
ejpam-6178	172	1	[	[	X
ejpam-6178	172	2	a]s	a]s	ADJ
ejpam-6178	172	3	∗	∗	NOUN
ejpam-6178	172	4	[	[	X
ejpam-6178	172	5	b]s	b]s	NOUN
ejpam-6178	172	6	∈	∈	PROPN
ejpam-6178	172	7	w	w	PROPN
ejpam-6178	172	8	which	which	PRON
ejpam-6178	172	9	implies	imply	VERB
ejpam-6178	172	10	that	that	SCONJ
ejpam-6178	172	11	a	a	DET
ejpam-6178	172	12	◦	◦	NOUN
ejpam-6178	172	13	b	b	X
ejpam-6178	172	14	∈	∈	PROPN
ejpam-6178	172	15	φ−1(w	φ−1(w	NOUN
ejpam-6178	172	16	)	)	PUNCT
ejpam-6178	172	17	∈	∈	PROPN
ejpam-6178	172	18	τ	τ	X
ejpam-6178	172	19	.	.	PUNCT
ejpam-6178	173	1	since	since	SCONJ
ejpam-6178	173	2	(	(	PUNCT
ejpam-6178	173	3	x	x	X
ejpam-6178	173	4	,	,	PUNCT
ejpam-6178	173	5	◦	◦	NOUN
ejpam-6178	173	6	,	,	PUNCT
ejpam-6178	173	7	τ	τ	X
ejpam-6178	173	8	)	)	PUNCT
ejpam-6178	173	9	is	be	AUX
ejpam-6178	173	10	a	a	DET
ejpam-6178	173	11	tdbalgebra	tdbalgebra	NOUN
ejpam-6178	173	12	,	,	PUNCT
ejpam-6178	173	13	by	by	ADP
ejpam-6178	173	14	theorem	theorem	NOUN
ejpam-6178	173	15	8	8	NUM
ejpam-6178	173	16	,	,	PUNCT
ejpam-6178	173	17	there	there	PRON
ejpam-6178	173	18	exist	exist	VERB
ejpam-6178	173	19	neighborhoods	neighborhood	NOUN
ejpam-6178	173	20	u(a	u(a	NOUN
ejpam-6178	173	21	)	)	PUNCT
ejpam-6178	173	22	and	and	CCONJ
ejpam-6178	173	23	v	v	NOUN
ejpam-6178	173	24	(	(	PUNCT
ejpam-6178	173	25	b	b	NOUN
ejpam-6178	173	26	)	)	PUNCT
ejpam-6178	173	27	of	of	ADP
ejpam-6178	173	28	a	a	PRON
ejpam-6178	173	29	and	and	CCONJ
ejpam-6178	173	30	b	b	NOUN
ejpam-6178	173	31	,	,	PUNCT
ejpam-6178	173	32	respectively	respectively	ADV
ejpam-6178	173	33	,	,	PUNCT
ejpam-6178	173	34	such	such	ADJ
ejpam-6178	173	35	that	that	SCONJ
ejpam-6178	173	36	u(a	u(a	PROPN
ejpam-6178	173	37	)	)	PUNCT
ejpam-6178	173	38	◦	◦	NOUN
ejpam-6178	173	39	v	v	NUM
ejpam-6178	173	40	(	(	PUNCT
ejpam-6178	173	41	b	b	NOUN
ejpam-6178	173	42	)	)	PUNCT
ejpam-6178	173	43	⊆	⊆	NUM
ejpam-6178	173	44	φ−1(w	φ−1(w	NOUN
ejpam-6178	173	45	)	)	PUNCT
ejpam-6178	173	46	.	.	PUNCT
ejpam-6178	174	1	moreover	moreover	ADV
ejpam-6178	174	2	,	,	PUNCT
ejpam-6178	174	3	φ(u(a	φ(u(a	PROPN
ejpam-6178	174	4	)	)	PUNCT
ejpam-6178	174	5	)	)	PUNCT
ejpam-6178	174	6	,	,	PUNCT
ejpam-6178	175	1	φ(v	φ(v	PROPN
ejpam-6178	175	2	(	(	PUNCT
ejpam-6178	175	3	b	b	NOUN
ejpam-6178	175	4	)	)	PUNCT
ejpam-6178	175	5	)	)	PUNCT
ejpam-6178	176	1	∈	∈	PROPN
ejpam-6178	176	2	τs	τs	ADP
ejpam-6178	176	3	since	since	SCONJ
ejpam-6178	176	4	φ	φ	PROPN
ejpam-6178	176	5	is	be	AUX
ejpam-6178	176	6	open	open	ADJ
ejpam-6178	176	7	.	.	PUNCT
ejpam-6178	177	1	note	note	VERB
ejpam-6178	177	2	that	that	SCONJ
ejpam-6178	177	3	since	since	SCONJ
ejpam-6178	177	4	[	[	X
ejpam-6178	177	5	a]s	a]s	ADJ
ejpam-6178	177	6	=	=	SYM
ejpam-6178	177	7	φ(a	φ(a	ADJ
ejpam-6178	177	8	)	)	PUNCT
ejpam-6178	177	9	∈	∈	PROPN
ejpam-6178	177	10	φ(u(a	φ(u(a	PROPN
ejpam-6178	177	11	)	)	PUNCT
ejpam-6178	177	12	)	)	PUNCT
ejpam-6178	177	13	implying	imply	VERB
ejpam-6178	177	14	that	that	SCONJ
ejpam-6178	177	15	φ(u(a	φ(u(a	PROPN
ejpam-6178	177	16	)	)	PUNCT
ejpam-6178	177	17	)	)	PUNCT
ejpam-6178	177	18	is	be	AUX
ejpam-6178	177	19	a	a	DET
ejpam-6178	177	20	neighborhood	neighborhood	NOUN
ejpam-6178	177	21	of	of	ADP
ejpam-6178	177	22	[	[	X
ejpam-6178	177	23	a]s	a]s	ADJ
ejpam-6178	177	24	.	.	PUNCT
ejpam-6178	178	1	similarly	similarly	ADV
ejpam-6178	178	2	,	,	PUNCT
ejpam-6178	178	3	φ(v	φ(v	PROPN
ejpam-6178	178	4	(	(	PUNCT
ejpam-6178	178	5	b	b	NOUN
ejpam-6178	178	6	)	)	PUNCT
ejpam-6178	178	7	)	)	PUNCT
ejpam-6178	178	8	is	be	AUX
ejpam-6178	178	9	a	a	DET
ejpam-6178	178	10	neighborhood	neighborhood	NOUN
ejpam-6178	178	11	of	of	ADP
ejpam-6178	178	12	[	[	X
ejpam-6178	178	13	b]s	b]s	NOUN
ejpam-6178	178	14	.	.	PUNCT
ejpam-6178	179	1	now	now	ADV
ejpam-6178	179	2	φ(u(a	φ(u(a	PROPN
ejpam-6178	179	3	)	)	PUNCT
ejpam-6178	179	4	)	)	PUNCT
ejpam-6178	179	5	∗	∗	NOUN
ejpam-6178	179	6	φ(v	φ(v	NOUN
ejpam-6178	179	7	(	(	PUNCT
ejpam-6178	179	8	b	b	NOUN
ejpam-6178	179	9	)	)	PUNCT
ejpam-6178	179	10	)	)	PUNCT
ejpam-6178	180	1	=	=	PRON
ejpam-6178	180	2	{	{	PUNCT
ejpam-6178	180	3	φ(x	φ(x	NOUN
ejpam-6178	180	4	)	)	PUNCT
ejpam-6178	180	5	∗	∗	NOUN
ejpam-6178	180	6	φ(y	φ(y	NOUN
ejpam-6178	180	7	)	)	PUNCT
ejpam-6178	181	1	|	|	ADV
ejpam-6178	181	2	x	x	SYM
ejpam-6178	181	3	∈	∈	PROPN
ejpam-6178	181	4	u(a	u(a	PROPN
ejpam-6178	181	5	)	)	PUNCT
ejpam-6178	181	6	,	,	PUNCT
ejpam-6178	181	7	y	y	PROPN
ejpam-6178	181	8	∈	∈	PROPN
ejpam-6178	181	9	v	v	ADP
ejpam-6178	181	10	(	(	PUNCT
ejpam-6178	181	11	b	b	NOUN
ejpam-6178	181	12	)	)	PUNCT
ejpam-6178	181	13	}	}	PUNCT
ejpam-6178	181	14	=	=	SYM
ejpam-6178	181	15	{	{	PUNCT
ejpam-6178	181	16	φ(x	φ(x	PROPN
ejpam-6178	181	17	◦	◦	PROPN
ejpam-6178	181	18	y	y	NOUN
ejpam-6178	181	19	)	)	PUNCT
ejpam-6178	181	20	|	|	ADV
ejpam-6178	181	21	x	x	PART
ejpam-6178	181	22	◦	◦	NOUN
ejpam-6178	181	23	y	y	PROPN
ejpam-6178	181	24	∈	∈	PROPN
ejpam-6178	181	25	u(a	u(a	PROPN
ejpam-6178	181	26	)	)	PUNCT
ejpam-6178	181	27	◦	◦	NOUN
ejpam-6178	181	28	v	v	NUM
ejpam-6178	181	29	(	(	PUNCT
ejpam-6178	181	30	b	b	NOUN
ejpam-6178	181	31	)	)	PUNCT
ejpam-6178	181	32	}	}	PUNCT
ejpam-6178	181	33	=	=	SYM
ejpam-6178	181	34	φ(u(a	φ(u(a	PROPN
ejpam-6178	181	35	)	)	PUNCT
ejpam-6178	181	36	◦	◦	NOUN
ejpam-6178	181	37	v	v	NUM
ejpam-6178	181	38	(	(	PUNCT
ejpam-6178	181	39	b	b	NOUN
ejpam-6178	181	40	)	)	PUNCT
ejpam-6178	181	41	)	)	PUNCT
ejpam-6178	182	1	⊆	⊆	NUM
ejpam-6178	182	2	φ(φ−1(w	φ(φ−1(w	NUM
ejpam-6178	182	3	)	)	PUNCT
ejpam-6178	182	4	)	)	PUNCT
ejpam-6178	183	1	=	=	PUNCT
ejpam-6178	183	2	w	w	PROPN
ejpam-6178	183	3	since	since	SCONJ
ejpam-6178	183	4	φ	φ	PROPN
ejpam-6178	183	5	is	be	AUX
ejpam-6178	183	6	onto	onto	ADP
ejpam-6178	183	7	.	.	PUNCT
ejpam-6178	184	1	by	by	ADP
ejpam-6178	184	2	theorem	theorem	NOUN
ejpam-6178	184	3	8	8	NUM
ejpam-6178	184	4	,	,	PUNCT
ejpam-6178	184	5	(	(	PUNCT
ejpam-6178	184	6	x	x	X
ejpam-6178	184	7	/	/	SYM
ejpam-6178	184	8	s	s	PROPN
ejpam-6178	184	9	,	,	PUNCT
ejpam-6178	184	10	∗	∗	NOUN
ejpam-6178	184	11	,	,	PUNCT
ejpam-6178	184	12	τs	τs	NOUN
ejpam-6178	184	13	)	)	PUNCT
ejpam-6178	184	14	is	be	AUX
ejpam-6178	184	15	a	a	DET
ejpam-6178	184	16	tdb	tdb	NOUN
ejpam-6178	184	17	-	-	NOUN
ejpam-6178	184	18	algebra	algebra	NOUN
ejpam-6178	184	19	.	.	PUNCT
ejpam-6178	185	1	the	the	DET
ejpam-6178	185	2	next	next	ADJ
ejpam-6178	185	3	example	example	NOUN
ejpam-6178	185	4	illustrates	illustrate	VERB
ejpam-6178	185	5	that	that	SCONJ
ejpam-6178	185	6	not	not	PART
ejpam-6178	185	7	all	all	DET
ejpam-6178	185	8	image	image	NOUN
ejpam-6178	185	9	of	of	ADP
ejpam-6178	185	10	a	a	DET
ejpam-6178	185	11	subset	subset	NOUN
ejpam-6178	185	12	of	of	ADP
ejpam-6178	185	13	a	a	DET
ejpam-6178	185	14	tdb	tdb	NOUN
ejpam-6178	185	15	-	-	NOUN
ejpam-6178	185	16	algebra	algebra	NOUN
ejpam-6178	185	17	is	be	AUX
ejpam-6178	185	18	open	open	ADJ
ejpam-6178	185	19	.	.	PUNCT
ejpam-6178	186	1	example	example	NOUN
ejpam-6178	186	2	4	4	NUM
ejpam-6178	186	3	.	.	X
ejpam-6178	187	1	consider	consider	VERB
ejpam-6178	187	2	example	example	NOUN
ejpam-6178	187	3	3	3	NUM
ejpam-6178	187	4	.	.	X
ejpam-6178	187	5	notice	notice	VERB
ejpam-6178	187	6	that	that	SCONJ
ejpam-6178	187	7	{	{	PUNCT
ejpam-6178	187	8	a	a	DET
ejpam-6178	187	9	,	,	PUNCT
ejpam-6178	187	10	b	b	NOUN
ejpam-6178	187	11	,	,	PUNCT
ejpam-6178	187	12	c	c	NOUN
ejpam-6178	187	13	}	}	PUNCT
ejpam-6178	187	14	⊂	⊂	PROPN
ejpam-6178	187	15	x	x	X
ejpam-6178	187	16	,	,	PUNCT
ejpam-6178	187	17	however	however	ADV
ejpam-6178	187	18	,	,	PUNCT
ejpam-6178	187	19	φ({a	φ({a	PROPN
ejpam-6178	187	20	,	,	PUNCT
ejpam-6178	187	21	b	b	PROPN
ejpam-6178	187	22	,	,	PUNCT
ejpam-6178	187	23	c	c	NOUN
ejpam-6178	187	24	}	}	PUNCT
ejpam-6178	187	25	)	)	PUNCT
ejpam-6178	188	1	=	=	PRON
ejpam-6178	188	2	{	{	PUNCT
ejpam-6178	188	3	{	{	PUNCT
ejpam-6178	188	4	a	a	NOUN
ejpam-6178	188	5	}	}	PUNCT
ejpam-6178	188	6	,	,	PUNCT
ejpam-6178	188	7	{	{	PUNCT
ejpam-6178	188	8	b	b	NOUN
ejpam-6178	188	9	}	}	PUNCT
ejpam-6178	188	10	,	,	PUNCT
ejpam-6178	188	11	{	{	PUNCT
ejpam-6178	188	12	c	c	X
ejpam-6178	188	13	}	}	PUNCT
ejpam-6178	188	14	}	}	PUNCT
ejpam-6178	188	15	is	be	AUX
ejpam-6178	188	16	not	not	PART
ejpam-6178	188	17	open	open	ADJ
ejpam-6178	188	18	in	in	ADP
ejpam-6178	188	19	x	x	X
ejpam-6178	188	20	/	/	SYM
ejpam-6178	188	21	s.	s.	PROPN
ejpam-6178	188	22	the	the	DET
ejpam-6178	188	23	next	next	PROPN
ejpam-6178	188	24	theorem	theorem	NOUN
ejpam-6178	188	25	says	say	VERB
ejpam-6178	188	26	about	about	ADP
ejpam-6178	188	27	the	the	DET
ejpam-6178	188	28	image	image	NOUN
ejpam-6178	188	29	of	of	ADP
ejpam-6178	188	30	a	a	DET
ejpam-6178	188	31	subset	subset	NOUN
ejpam-6178	188	32	of	of	ADP
ejpam-6178	188	33	a	a	DET
ejpam-6178	188	34	tdb	tdb	NOUN
ejpam-6178	188	35	-	-	NOUN
ejpam-6178	188	36	algebra	algebra	NOUN
ejpam-6178	188	37	when	when	SCONJ
ejpam-6178	188	38	a	a	DET
ejpam-6178	188	39	particular	particular	ADJ
ejpam-6178	188	40	property	property	NOUN
ejpam-6178	188	41	that	that	PRON
ejpam-6178	188	42	the	the	DET
ejpam-6178	188	43	normal	normal	ADJ
ejpam-6178	188	44	db	db	NOUN
ejpam-6178	188	45	-	-	PUNCT
ejpam-6178	188	46	subalgebra	subalgebra	NOUN
ejpam-6178	188	47	should	should	AUX
ejpam-6178	188	48	hold	hold	VERB
ejpam-6178	188	49	and	and	CCONJ
ejpam-6178	188	50	its	its	PRON
ejpam-6178	188	51	corresponding	corresponding	ADJ
ejpam-6178	188	52	implication	implication	NOUN
ejpam-6178	188	53	.	.	PUNCT
ejpam-6178	189	1	theorem	theorem	NOUN
ejpam-6178	189	2	13	13	NUM
ejpam-6178	189	3	.	.	PUNCT
ejpam-6178	190	1	let	let	VERB
ejpam-6178	190	2	s	s	PRON
ejpam-6178	190	3	be	be	AUX
ejpam-6178	190	4	open	open	ADJ
ejpam-6178	190	5	in	in	ADP
ejpam-6178	190	6	a	a	DET
ejpam-6178	190	7	tdb	tdb	NOUN
ejpam-6178	190	8	-	-	NOUN
ejpam-6178	190	9	algebra	algebra	NOUN
ejpam-6178	190	10	(	(	PUNCT
ejpam-6178	190	11	x	x	X
ejpam-6178	190	12	,	,	PUNCT
ejpam-6178	190	13	◦	◦	NOUN
ejpam-6178	190	14	,	,	PUNCT
ejpam-6178	190	15	τ	τ	PROPN
ejpam-6178	190	16	)	)	PUNCT
ejpam-6178	190	17	.	.	PUNCT
ejpam-6178	191	1	then	then	ADV
ejpam-6178	191	2	φ(a	φ(a	ADJ
ejpam-6178	191	3	)	)	PUNCT
ejpam-6178	191	4	is	be	AUX
ejpam-6178	191	5	open	open	ADJ
ejpam-6178	191	6	in	in	ADP
ejpam-6178	191	7	x	x	X
ejpam-6178	191	8	/	/	SYM
ejpam-6178	191	9	s	s	NOUN
ejpam-6178	191	10	for	for	ADP
ejpam-6178	191	11	every	every	DET
ejpam-6178	191	12	subset	subset	NOUN
ejpam-6178	191	13	a	a	PRON
ejpam-6178	191	14	of	of	ADP
ejpam-6178	191	15	x	x	PRON
ejpam-6178	191	16	where	where	SCONJ
ejpam-6178	191	17	φ	φ	PROPN
ejpam-6178	191	18	is	be	AUX
ejpam-6178	191	19	a	a	DET
ejpam-6178	191	20	natural	natural	ADJ
ejpam-6178	191	21	db	db	NOUN
ejpam-6178	191	22	-	-	PUNCT
ejpam-6178	191	23	homomorphism	homomorphism	NOUN
ejpam-6178	191	24	.	.	PUNCT
ejpam-6178	192	1	in	in	ADP
ejpam-6178	192	2	particular	particular	ADJ
ejpam-6178	192	3	,	,	PUNCT
ejpam-6178	192	4	φ	φ	PROPN
ejpam-6178	192	5	is	be	AUX
ejpam-6178	192	6	an	an	DET
ejpam-6178	192	7	open	open	ADJ
ejpam-6178	192	8	mapping	mapping	NOUN
ejpam-6178	192	9	.	.	PUNCT
ejpam-6178	193	1	proof	proof	NOUN
ejpam-6178	193	2	.	.	PUNCT
ejpam-6178	194	1	let	let	VERB
ejpam-6178	194	2	a	a	DET
ejpam-6178	194	3	⊆	⊆	NUM
ejpam-6178	194	4	x.	x.	NOUN
ejpam-6178	194	5	to	to	PART
ejpam-6178	194	6	show	show	VERB
ejpam-6178	194	7	that	that	SCONJ
ejpam-6178	194	8	φ(a	φ(a	ADJ
ejpam-6178	194	9	)	)	PUNCT
ejpam-6178	194	10	is	be	AUX
ejpam-6178	194	11	open	open	ADJ
ejpam-6178	194	12	,	,	PUNCT
ejpam-6178	194	13	it	it	PRON
ejpam-6178	194	14	should	should	AUX
ejpam-6178	194	15	be	be	AUX
ejpam-6178	194	16	proven	prove	VERB
ejpam-6178	194	17	that	that	SCONJ
ejpam-6178	194	18	φ−1(φ(a	φ−1(φ(a	ADV
ejpam-6178	194	19	)	)	PUNCT
ejpam-6178	194	20	)	)	PUNCT
ejpam-6178	194	21	is	be	AUX
ejpam-6178	194	22	open	open	ADJ
ejpam-6178	194	23	in	in	ADP
ejpam-6178	194	24	x	x	PROPN
ejpam-6178	194	25	/	/	SYM
ejpam-6178	194	26	s.	s.	PROPN
ejpam-6178	194	27	note	note	VERB
ejpam-6178	194	28	that	that	SCONJ
ejpam-6178	194	29	φ−1(φ(a	φ−1(φ(a	ADV
ejpam-6178	194	30	)	)	PUNCT
ejpam-6178	194	31	)	)	PUNCT
ejpam-6178	195	1	=	=	PRON
ejpam-6178	195	2	{	{	PUNCT
ejpam-6178	195	3	x	x	PUNCT
ejpam-6178	195	4	∈	∈	PROPN
ejpam-6178	195	5	x	x	X
ejpam-6178	195	6	|	|	ADV
ejpam-6178	195	7	φ(x	φ(x	NOUN
ejpam-6178	195	8	)	)	PUNCT
ejpam-6178	195	9	∈	∈	NOUN
ejpam-6178	195	10	φ(a	φ(a	ADJ
ejpam-6178	195	11	)	)	PUNCT
ejpam-6178	195	12	}	}	PUNCT
ejpam-6178	195	13	.	.	PUNCT
ejpam-6178	196	1	let	let	VERB
ejpam-6178	196	2	x	x	PUNCT
ejpam-6178	196	3	∈	∈	VERB
ejpam-6178	196	4	φ−1(φ(a	φ−1(φ(a	NOUN
ejpam-6178	196	5	)	)	PUNCT
ejpam-6178	196	6	)	)	PUNCT
ejpam-6178	196	7	.	.	PUNCT
ejpam-6178	197	1	then	then	ADV
ejpam-6178	197	2	[	[	X
ejpam-6178	197	3	x]s	x]s	NOUN
ejpam-6178	197	4	=	=	SYM
ejpam-6178	197	5	φ(x	φ(x	NOUN
ejpam-6178	197	6	)	)	PUNCT
ejpam-6178	197	7	∈	∈	NOUN
ejpam-6178	197	8	φ(a	φ(a	ADJ
ejpam-6178	197	9	)	)	PUNCT
ejpam-6178	197	10	.	.	PUNCT
ejpam-6178	198	1	hence	hence	ADV
ejpam-6178	198	2	,	,	PUNCT
ejpam-6178	198	3	[	[	X
ejpam-6178	198	4	x]s	x]s	NOUN
ejpam-6178	198	5	=	=	SYM
ejpam-6178	198	6	φ(a	φ(a	ADJ
ejpam-6178	198	7	)	)	PUNCT
ejpam-6178	198	8	=	=	PUNCT
ejpam-6178	199	1	[	[	X
ejpam-6178	199	2	a]s	a]s	X
ejpam-6178	199	3	,	,	PUNCT
ejpam-6178	199	4	for	for	ADP
ejpam-6178	199	5	some	some	PRON
ejpam-6178	199	6	a	a	DET
ejpam-6178	199	7	∈	∈	NOUN
ejpam-6178	199	8	a.	a.	NOUN
ejpam-6178	199	9	thus	thus	ADV
ejpam-6178	199	10	x	x	SYM
ejpam-6178	199	11	∼s	∼s	PROPN
ejpam-6178	199	12	a	a	PRON
ejpam-6178	199	13	by	by	ADP
ejpam-6178	199	14	lemma	lemma	PROPN
ejpam-6178	199	15	1	1	NUM
ejpam-6178	199	16	.	.	PUNCT
ejpam-6178	199	17	that	that	PRON
ejpam-6178	199	18	is	be	AUX
ejpam-6178	199	19	,	,	PUNCT
ejpam-6178	199	20	x	x	PUNCT
ejpam-6178	199	21	◦	◦	VERB
ejpam-6178	199	22	a	a	PRON
ejpam-6178	199	23	,	,	PUNCT
ejpam-6178	199	24	a	a	DET
ejpam-6178	199	25	◦	◦	NOUN
ejpam-6178	199	26	x	x	SYM
ejpam-6178	199	27	∈	∈	PROPN
ejpam-6178	199	28	s.	s.	PROPN
ejpam-6178	199	29	since	since	SCONJ
ejpam-6178	199	30	s	s	PROPN
ejpam-6178	199	31	is	be	AUX
ejpam-6178	199	32	open	open	ADJ
ejpam-6178	199	33	in	in	ADP
ejpam-6178	199	34	x	x	PUNCT
ejpam-6178	199	35	and	and	CCONJ
ejpam-6178	199	36	x	x	X
ejpam-6178	199	37	is	be	AUX
ejpam-6178	199	38	a	a	DET
ejpam-6178	199	39	tdb	tdb	NOUN
ejpam-6178	199	40	-	-	NOUN
ejpam-6178	199	41	algebra	algebra	NOUN
ejpam-6178	199	42	,	,	PUNCT
ejpam-6178	199	43	it	it	PRON
ejpam-6178	199	44	follows	follow	VERB
ejpam-6178	199	45	that	that	SCONJ
ejpam-6178	199	46	there	there	PRON
ejpam-6178	199	47	exist	exist	VERB
ejpam-6178	199	48	neighborhoods	neighborhood	NOUN
ejpam-6178	199	49	u1(x	u1(x	ADV
ejpam-6178	199	50	)	)	PUNCT
ejpam-6178	199	51	and	and	CCONJ
ejpam-6178	199	52	u2(x	u2(x	NUM
ejpam-6178	199	53	)	)	PUNCT
ejpam-6178	199	54	for	for	ADP
ejpam-6178	199	55	x	x	NOUN
ejpam-6178	199	56	,	,	PUNCT
ejpam-6178	199	57	and	and	CCONJ
ejpam-6178	199	58	u1(a	u1(a	NUM
ejpam-6178	199	59	)	)	PUNCT
ejpam-6178	199	60	and	and	CCONJ
ejpam-6178	199	61	u2(a	u2(a	NOUN
ejpam-6178	199	62	)	)	PUNCT
ejpam-6178	199	63	for	for	ADP
ejpam-6178	199	64	a	a	DET
ejpam-6178	199	65	such	such	ADJ
ejpam-6178	199	66	that	that	DET
ejpam-6178	199	67	u1(x	u1(x	NOUN
ejpam-6178	199	68	)	)	PUNCT
ejpam-6178	199	69	◦	◦	NOUN
ejpam-6178	199	70	u1(a	u1(a	NUM
ejpam-6178	199	71	)	)	PUNCT
ejpam-6178	199	72	⊆	⊆	NUM
ejpam-6178	199	73	s	s	NOUN
ejpam-6178	199	74	and	and	CCONJ
ejpam-6178	199	75	u2(a	u2(a	NOUN
ejpam-6178	199	76	)	)	PUNCT
ejpam-6178	199	77	◦	◦	NOUN
ejpam-6178	199	78	u2(x	u2(x	X
ejpam-6178	199	79	)	)	PUNCT
ejpam-6178	199	80	⊆	⊆	NUM
ejpam-6178	199	81	s	s	NOUN
ejpam-6178	199	82	(	(	PUNCT
ejpam-6178	199	83	by	by	ADP
ejpam-6178	199	84	theorem	theorem	NOUN
ejpam-6178	199	85	8)	8)	NUM
ejpam-6178	199	86	.	.	PUNCT
ejpam-6178	200	1	then	then	ADV
ejpam-6178	200	2	(	(	PUNCT
ejpam-6178	200	3	u1(x)∩u2(x	u1(x)∩u2(x	NOUN
ejpam-6178	200	4	)	)	PUNCT
ejpam-6178	200	5	)	)	PUNCT
ejpam-6178	201	1	◦	◦	NOUN
ejpam-6178	201	2	u1(a	u1(a	NUM
ejpam-6178	201	3	)	)	PUNCT
ejpam-6178	201	4	⊆	⊆	PROPN
ejpam-6178	201	5	r.	r.	PROPN
ejpam-6178	201	6	nuñez	nuñez	PROPN
ejpam-6178	201	7	,	,	PUNCT
ejpam-6178	201	8	k.	k.	PROPN
ejpam-6178	201	9	b.	b.	PROPN
ejpam-6178	201	10	fuentes	fuentes	PROPN
ejpam-6178	201	11	/	/	SYM
ejpam-6178	201	12	eur	eur	PROPN
ejpam-6178	201	13	.	.	PUNCT
ejpam-6178	202	1	j.	j.	PROPN
ejpam-6178	202	2	pure	pure	PROPN
ejpam-6178	202	3	appl	appl	PROPN
ejpam-6178	202	4	.	.	PROPN
ejpam-6178	202	5	math	math	PROPN
ejpam-6178	202	6	,	,	PUNCT
ejpam-6178	202	7	18	18	NUM
ejpam-6178	202	8	(	(	PUNCT
ejpam-6178	202	9	4	4	NUM
ejpam-6178	202	10	)	)	PUNCT
ejpam-6178	202	11	(	(	PUNCT
ejpam-6178	202	12	2025	2025	NUM
ejpam-6178	202	13	)	)	PUNCT
ejpam-6178	202	14	,	,	PUNCT
ejpam-6178	202	15	6178	6178	NUM
ejpam-6178	202	16	7	7	NUM
ejpam-6178	202	17	of	of	ADP
ejpam-6178	202	18	15	15	NUM
ejpam-6178	202	19	u1(x)	u1(x)	PROPN
ejpam-6178	202	20	◦	◦	NOUN
ejpam-6178	202	21	u1(a	u1(a	NOUN
ejpam-6178	202	22	)	)	PUNCT
ejpam-6178	202	23	⊆	⊆	NUM
ejpam-6178	202	24	s	s	NOUN
ejpam-6178	202	25	and	and	CCONJ
ejpam-6178	202	26	u2(a)	u2(a)	PROPN
ejpam-6178	202	27	◦	◦	NOUN
ejpam-6178	202	28	(u1(x)∩u2(x	(u1(x)∩u2(x	NOUN
ejpam-6178	202	29	)	)	PUNCT
ejpam-6178	202	30	)	)	PUNCT
ejpam-6178	203	1	⊆	⊆	NUM
ejpam-6178	203	2	u2(a)	u2(a)	NOUN
ejpam-6178	203	3	◦	◦	NOUN
ejpam-6178	203	4	u2(x	u2(x	NOUN
ejpam-6178	203	5	)	)	PUNCT
ejpam-6178	203	6	⊆	⊆	NUM
ejpam-6178	203	7	s.	s.	PROPN
ejpam-6178	203	8	since	since	SCONJ
ejpam-6178	203	9	u1(x	u1(x	PROPN
ejpam-6178	203	10	)	)	PUNCT
ejpam-6178	203	11	,	,	PUNCT
ejpam-6178	203	12	u2(x	u2(x	SYM
ejpam-6178	203	13	)	)	PUNCT
ejpam-6178	203	14	∈	∈	PROPN
ejpam-6178	203	15	τ	τ	X
ejpam-6178	203	16	,	,	PUNCT
ejpam-6178	203	17	it	it	PRON
ejpam-6178	203	18	follows	follow	VERB
ejpam-6178	203	19	that	that	SCONJ
ejpam-6178	203	20	u1(x	u1(x	NOUN
ejpam-6178	203	21	)	)	PUNCT
ejpam-6178	203	22	∩	∩	NOUN
ejpam-6178	203	23	u2(x	u2(x	SYM
ejpam-6178	203	24	)	)	PUNCT
ejpam-6178	203	25	∈	∈	PROPN
ejpam-6178	204	1	τ	τ	X
ejpam-6178	204	2	.	.	PUNCT
ejpam-6178	205	1	let	let	VERB
ejpam-6178	205	2	y	y	PRON
ejpam-6178	205	3	∈	∈	NOUN
ejpam-6178	205	4	u1(x	u1(x	NOUN
ejpam-6178	205	5	)	)	PUNCT
ejpam-6178	205	6	∩	∩	NOUN
ejpam-6178	205	7	u2(x	u2(x	NUM
ejpam-6178	205	8	)	)	PUNCT
ejpam-6178	205	9	.	.	PUNCT
ejpam-6178	206	1	then	then	ADV
ejpam-6178	206	2	y	y	PROPN
ejpam-6178	206	3	◦	◦	VERB
ejpam-6178	206	4	a	a	PRON
ejpam-6178	206	5	,	,	PUNCT
ejpam-6178	206	6	a	a	DET
ejpam-6178	206	7	◦	◦	NOUN
ejpam-6178	206	8	y	y	PROPN
ejpam-6178	206	9	∈	∈	PROPN
ejpam-6178	206	10	s.	s.	PROPN
ejpam-6178	206	11	hence	hence	ADV
ejpam-6178	206	12	,	,	PUNCT
ejpam-6178	206	13	y	y	PROPN
ejpam-6178	206	14	∼s	∼s	PROPN
ejpam-6178	206	15	a.	a.	NOUN
ejpam-6178	206	16	thus	thus	ADV
ejpam-6178	206	17	φ(y	φ(y	VERB
ejpam-6178	206	18	)	)	PUNCT
ejpam-6178	206	19	=	=	PUNCT
ejpam-6178	207	1	[	[	X
ejpam-6178	207	2	y]s	y]s	X
ejpam-6178	207	3	=	=	PUNCT
ejpam-6178	208	1	[	[	X
ejpam-6178	208	2	a]s	a]s	ADJ
ejpam-6178	208	3	=	=	SYM
ejpam-6178	208	4	φ(a	φ(a	ADJ
ejpam-6178	208	5	)	)	PUNCT
ejpam-6178	208	6	∈	∈	PROPN
ejpam-6178	208	7	φ(a	φ(a	ADJ
ejpam-6178	208	8	)	)	PUNCT
ejpam-6178	208	9	.	.	PUNCT
ejpam-6178	209	1	this	this	PRON
ejpam-6178	209	2	implies	imply	VERB
ejpam-6178	209	3	that	that	SCONJ
ejpam-6178	209	4	y	y	PROPN
ejpam-6178	209	5	∈	∈	PROPN
ejpam-6178	209	6	φ−1(φ(a	φ−1(φ(a	ADV
ejpam-6178	209	7	)	)	PUNCT
ejpam-6178	209	8	)	)	PUNCT
ejpam-6178	209	9	.	.	PUNCT
ejpam-6178	210	1	hence	hence	ADV
ejpam-6178	210	2	u1(x	u1(x	NOUN
ejpam-6178	210	3	)	)	PUNCT
ejpam-6178	211	1	∩	∩	NOUN
ejpam-6178	211	2	u2(x	u2(x	SYM
ejpam-6178	211	3	)	)	PUNCT
ejpam-6178	211	4	⊆	⊆	NUM
ejpam-6178	211	5	φ−1(φ(a	φ−1(φ(a	NOUN
ejpam-6178	211	6	)	)	PUNCT
ejpam-6178	211	7	)	)	PUNCT
ejpam-6178	211	8	.	.	PUNCT
ejpam-6178	212	1	by	by	ADP
ejpam-6178	212	2	remark	remark	NOUN
ejpam-6178	212	3	2	2	NUM
ejpam-6178	212	4	,	,	PUNCT
ejpam-6178	212	5	φ−1(φ(a	φ−1(φ(a	ADV
ejpam-6178	212	6	)	)	PUNCT
ejpam-6178	212	7	)	)	PUNCT
ejpam-6178	212	8	is	be	AUX
ejpam-6178	212	9	open	open	ADJ
ejpam-6178	212	10	in	in	ADP
ejpam-6178	212	11	x	x	PUNCT
ejpam-6178	212	12	which	which	PRON
ejpam-6178	212	13	proves	prove	VERB
ejpam-6178	212	14	that	that	SCONJ
ejpam-6178	212	15	φ(a	φ(a	ADJ
ejpam-6178	212	16	)	)	PUNCT
ejpam-6178	212	17	is	be	AUX
ejpam-6178	212	18	open	open	ADJ
ejpam-6178	212	19	in	in	ADP
ejpam-6178	212	20	x	x	X
ejpam-6178	212	21	/	/	SYM
ejpam-6178	212	22	s.	s.	PROPN
ejpam-6178	212	23	in	in	ADP
ejpam-6178	212	24	particular	particular	ADJ
ejpam-6178	212	25	,	,	PUNCT
ejpam-6178	212	26	if	if	SCONJ
ejpam-6178	212	27	a	a	PRON
ejpam-6178	212	28	is	be	AUX
ejpam-6178	212	29	open	open	ADJ
ejpam-6178	212	30	,	,	PUNCT
ejpam-6178	212	31	φ	φ	PROPN
ejpam-6178	212	32	is	be	AUX
ejpam-6178	212	33	an	an	DET
ejpam-6178	212	34	open	open	ADJ
ejpam-6178	212	35	mapping	mapping	NOUN
ejpam-6178	212	36	.	.	PUNCT
ejpam-6178	213	1	corollary	corollary	ADJ
ejpam-6178	213	2	1	1	NUM
ejpam-6178	213	3	is	be	AUX
ejpam-6178	213	4	a	a	DET
ejpam-6178	213	5	consequence	consequence	NOUN
ejpam-6178	213	6	of	of	ADP
ejpam-6178	213	7	theorem	theorem	ADJ
ejpam-6178	213	8	13	13	NUM
ejpam-6178	213	9	and	and	CCONJ
ejpam-6178	213	10	theorem	theorem	VERB
ejpam-6178	213	11	12	12	NUM
ejpam-6178	213	12	.	.	PUNCT
ejpam-6178	214	1	corollary	corollary	ADJ
ejpam-6178	214	2	1	1	NUM
ejpam-6178	214	3	.	.	PUNCT
ejpam-6178	215	1	let	let	VERB
ejpam-6178	215	2	s	s	PRON
ejpam-6178	215	3	be	be	AUX
ejpam-6178	215	4	open	open	ADJ
ejpam-6178	215	5	in	in	ADP
ejpam-6178	215	6	a	a	DET
ejpam-6178	215	7	tdb	tdb	NOUN
ejpam-6178	215	8	-	-	NOUN
ejpam-6178	215	9	algebra	algebra	NOUN
ejpam-6178	215	10	(	(	PUNCT
ejpam-6178	215	11	x	x	X
ejpam-6178	215	12	,	,	PUNCT
ejpam-6178	215	13	◦	◦	NOUN
ejpam-6178	215	14	,	,	PUNCT
ejpam-6178	215	15	τ	τ	PROPN
ejpam-6178	215	16	)	)	PUNCT
ejpam-6178	215	17	.	.	PUNCT
ejpam-6178	216	1	then	then	ADV
ejpam-6178	216	2	(	(	PUNCT
ejpam-6178	216	3	x	x	X
ejpam-6178	216	4	/	/	SYM
ejpam-6178	216	5	s	s	PROPN
ejpam-6178	216	6	,	,	PUNCT
ejpam-6178	216	7	∗	∗	NOUN
ejpam-6178	216	8	,	,	PUNCT
ejpam-6178	216	9	τs	τs	NOUN
ejpam-6178	216	10	)	)	PUNCT
ejpam-6178	216	11	is	be	AUX
ejpam-6178	216	12	a	a	DET
ejpam-6178	216	13	tdb	tdb	NOUN
ejpam-6178	216	14	-	-	NOUN
ejpam-6178	216	15	algebra	algebra	NOUN
ejpam-6178	216	16	.	.	PUNCT
ejpam-6178	217	1	definition	definition	NOUN
ejpam-6178	217	2	12	12	NUM
ejpam-6178	217	3	.	.	PUNCT
ejpam-6178	218	1	let	let	VERB
ejpam-6178	218	2	(	(	PUNCT
ejpam-6178	218	3	x	x	NOUN
ejpam-6178	218	4	,	,	PUNCT
ejpam-6178	218	5	◦	◦	NOUN
ejpam-6178	218	6	,	,	PUNCT
ejpam-6178	218	7	τ	τ	X
ejpam-6178	218	8	)	)	PUNCT
ejpam-6178	218	9	and	and	CCONJ
ejpam-6178	218	10	(	(	PUNCT
ejpam-6178	218	11	y	y	PROPN
ejpam-6178	218	12	,	,	PUNCT
ejpam-6178	218	13	∗	∗	NOUN
ejpam-6178	218	14	,	,	PUNCT
ejpam-6178	218	15	τ∗	τ∗	NOUN
ejpam-6178	218	16	)	)	PUNCT
ejpam-6178	218	17	be	be	VERB
ejpam-6178	218	18	tdb	tdb	NOUN
ejpam-6178	218	19	-	-	PUNCT
ejpam-6178	218	20	algebras	algebras	X
ejpam-6178	218	21	.	.	PUNCT
ejpam-6178	219	1	a	a	DET
ejpam-6178	219	2	mapping	mapping	NOUN
ejpam-6178	219	3	φ	φ	NOUN
ejpam-6178	219	4	:	:	PUNCT
ejpam-6178	219	5	x	x	X
ejpam-6178	219	6	→	→	SYM
ejpam-6178	219	7	y	y	PROPN
ejpam-6178	219	8	is	be	AUX
ejpam-6178	219	9	called	call	VERB
ejpam-6178	219	10	a	a	DET
ejpam-6178	219	11	topological	topological	ADJ
ejpam-6178	219	12	dual	dual	ADJ
ejpam-6178	219	13	b	b	NOUN
ejpam-6178	219	14	-	-	PUNCT
ejpam-6178	219	15	homomorphism	homomorphism	NOUN
ejpam-6178	219	16	(	(	PUNCT
ejpam-6178	219	17	tdb	tdb	PROPN
ejpam-6178	219	18	-	-	NOUN
ejpam-6178	219	19	homomorphism	homomorphism	NOUN
ejpam-6178	219	20	)	)	PUNCT
ejpam-6178	219	21	if	if	SCONJ
ejpam-6178	219	22	(	(	PUNCT
ejpam-6178	219	23	i	i	NOUN
ejpam-6178	219	24	)	)	PUNCT
ejpam-6178	219	25	φ	φ	PROPN
ejpam-6178	219	26	is	be	AUX
ejpam-6178	219	27	a	a	DET
ejpam-6178	219	28	db	db	NOUN
ejpam-6178	219	29	-	-	PUNCT
ejpam-6178	219	30	homomorphism	homomorphism	NOUN
ejpam-6178	219	31	from	from	ADP
ejpam-6178	219	32	(	(	PUNCT
ejpam-6178	219	33	x	x	NOUN
ejpam-6178	219	34	,	,	PUNCT
ejpam-6178	219	35	◦	◦	NOUN
ejpam-6178	219	36	,	,	PUNCT
ejpam-6178	219	37	1x	1x	NUM
ejpam-6178	219	38	)	)	PUNCT
ejpam-6178	219	39	to	to	ADP
ejpam-6178	219	40	(	(	PUNCT
ejpam-6178	219	41	y	y	PROPN
ejpam-6178	219	42	,	,	PUNCT
ejpam-6178	219	43	∗	∗	NOUN
ejpam-6178	219	44	,	,	PUNCT
ejpam-6178	219	45	1y	1y	NOUN
ejpam-6178	219	46	)	)	PUNCT
ejpam-6178	219	47	,	,	PUNCT
ejpam-6178	219	48	and	and	CCONJ
ejpam-6178	219	49	(	(	PUNCT
ejpam-6178	219	50	ii	ii	NOUN
ejpam-6178	219	51	)	)	PUNCT
ejpam-6178	219	52	φ	φ	PROPN
ejpam-6178	219	53	is	be	AUX
ejpam-6178	219	54	a	a	DET
ejpam-6178	219	55	continuous	continuous	ADJ
ejpam-6178	219	56	mapping	mapping	NOUN
ejpam-6178	219	57	from	from	ADP
ejpam-6178	219	58	(	(	PUNCT
ejpam-6178	219	59	x	x	NOUN
ejpam-6178	219	60	,	,	PUNCT
ejpam-6178	219	61	τ	τ	X
ejpam-6178	219	62	)	)	PUNCT
ejpam-6178	219	63	to	to	ADP
ejpam-6178	219	64	(	(	PUNCT
ejpam-6178	219	65	y	y	NOUN
ejpam-6178	219	66	,	,	PUNCT
ejpam-6178	219	67	τ∗	τ∗	NOUN
ejpam-6178	219	68	)	)	PUNCT
ejpam-6178	219	69	.	.	PUNCT
ejpam-6178	219	70	example	example	NOUN
ejpam-6178	220	1	5	5	NUM
ejpam-6178	220	2	.	.	PUNCT
ejpam-6178	220	3	consider	consider	VERB
ejpam-6178	220	4	the	the	DET
ejpam-6178	220	5	tdb	tdb	NOUN
ejpam-6178	220	6	-	-	NOUN
ejpam-6178	220	7	algebra	algebra	PROPN
ejpam-6178	220	8	(	(	PUNCT
ejpam-6178	220	9	x	x	X
ejpam-6178	220	10	,	,	PUNCT
ejpam-6178	220	11	◦	◦	NOUN
ejpam-6178	220	12	,	,	PUNCT
ejpam-6178	220	13	τ	τ	X
ejpam-6178	220	14	)	)	PUNCT
ejpam-6178	220	15	in	in	ADP
ejpam-6178	220	16	example	example	NOUN
ejpam-6178	220	17	2	2	NUM
ejpam-6178	220	18	.	.	PUNCT
ejpam-6178	220	19	define	define	VERB
ejpam-6178	220	20	a	a	DET
ejpam-6178	220	21	mapping	mapping	NOUN
ejpam-6178	220	22	φ	φ	NOUN
ejpam-6178	220	23	:	:	PUNCT
ejpam-6178	220	24	x	x	X
ejpam-6178	220	25	→	→	SYM
ejpam-6178	220	26	x	x	PUNCT
ejpam-6178	220	27	as	as	SCONJ
ejpam-6178	220	28	follows	follow	VERB
ejpam-6178	220	29	:	:	PUNCT
ejpam-6178	220	30	φ(1	φ(1	PROPN
ejpam-6178	220	31	)	)	PUNCT
ejpam-6178	220	32	=	=	SYM
ejpam-6178	220	33	1	1	NUM
ejpam-6178	220	34	,	,	PUNCT
ejpam-6178	220	35	φ(a	φ(a	ADJ
ejpam-6178	220	36	)	)	PUNCT
ejpam-6178	220	37	=	=	SYM
ejpam-6178	221	1	a	a	DET
ejpam-6178	221	2	,	,	PUNCT
ejpam-6178	221	3	φ(b	φ(b	PROPN
ejpam-6178	221	4	)	)	PUNCT
ejpam-6178	221	5	=	=	SYM
ejpam-6178	221	6	c	c	X
ejpam-6178	221	7	,	,	PUNCT
ejpam-6178	221	8	φ(c	φ(c	NOUN
ejpam-6178	221	9	)	)	PUNCT
ejpam-6178	221	10	=	=	SYM
ejpam-6178	221	11	b.	b.	PROPN
ejpam-6178	221	12	by	by	ADP
ejpam-6178	221	13	a	a	DET
ejpam-6178	221	14	program	program	NOUN
ejpam-6178	221	15	(	(	PUNCT
ejpam-6178	221	16	see	see	VERB
ejpam-6178	221	17	appendix	appendix	NOUN
ejpam-6178	221	18	)	)	PUNCT
ejpam-6178	221	19	,	,	PUNCT
ejpam-6178	221	20	φ	φ	PROPN
ejpam-6178	221	21	is	be	AUX
ejpam-6178	221	22	a	a	DET
ejpam-6178	221	23	db	db	NOUN
ejpam-6178	221	24	-	-	PUNCT
ejpam-6178	221	25	homomorphism	homomorphism	NOUN
ejpam-6178	221	26	.	.	PUNCT
ejpam-6178	222	1	by	by	ADP
ejpam-6178	222	2	manual	manual	ADJ
ejpam-6178	222	3	computations	computation	NOUN
ejpam-6178	222	4	φ	φ	X
ejpam-6178	222	5	is	be	AUX
ejpam-6178	222	6	a	a	DET
ejpam-6178	222	7	continuous	continuous	ADJ
ejpam-6178	222	8	mapping	mapping	NOUN
ejpam-6178	222	9	.	.	PUNCT
ejpam-6178	223	1	hence	hence	ADV
ejpam-6178	223	2	,	,	PUNCT
ejpam-6178	223	3	φ	φ	PROPN
ejpam-6178	223	4	is	be	AUX
ejpam-6178	223	5	a	a	DET
ejpam-6178	223	6	tdb	tdb	PROPN
ejpam-6178	223	7	-	-	NOUN
ejpam-6178	223	8	homomorphism	homomorphism	NOUN
ejpam-6178	223	9	.	.	PUNCT
ejpam-6178	224	1	definition	definition	NOUN
ejpam-6178	224	2	13	13	NUM
ejpam-6178	224	3	.	.	PUNCT
ejpam-6178	225	1	a	a	DET
ejpam-6178	225	2	tdb	tdb	PROPN
ejpam-6178	225	3	-	-	PROPN
ejpam-6178	225	4	homomorphism	homomorphism	NOUN
ejpam-6178	225	5	φ	φ	PROPN
ejpam-6178	225	6	is	be	AUX
ejpam-6178	225	7	said	say	VERB
ejpam-6178	225	8	to	to	PART
ejpam-6178	225	9	be	be	AUX
ejpam-6178	225	10	open	open	ADJ
ejpam-6178	225	11	if	if	SCONJ
ejpam-6178	225	12	φ	φ	PROPN
ejpam-6178	225	13	is	be	AUX
ejpam-6178	225	14	an	an	DET
ejpam-6178	225	15	open	open	ADJ
ejpam-6178	225	16	mapping	mapping	NOUN
ejpam-6178	225	17	of	of	ADP
ejpam-6178	225	18	the	the	DET
ejpam-6178	225	19	dual	dual	ADJ
ejpam-6178	225	20	b	b	NOUN
ejpam-6178	225	21	-	-	PUNCT
ejpam-6178	225	22	topological	topological	ADJ
ejpam-6178	225	23	spaces	space	NOUN
ejpam-6178	225	24	.	.	PUNCT
ejpam-6178	226	1	example	example	NOUN
ejpam-6178	226	2	6	6	NUM
ejpam-6178	226	3	.	.	PUNCT
ejpam-6178	227	1	consider	consider	VERB
ejpam-6178	227	2	the	the	DET
ejpam-6178	227	3	same	same	ADJ
ejpam-6178	227	4	tdb	tdb	NOUN
ejpam-6178	227	5	-	-	NOUN
ejpam-6178	227	6	homomorphism	homomorphism	NOUN
ejpam-6178	227	7	in	in	ADP
ejpam-6178	227	8	example	example	NOUN
ejpam-6178	227	9	5	5	NUM
ejpam-6178	227	10	.	.	PUNCT
ejpam-6178	227	11	by	by	ADP
ejpam-6178	227	12	manual	manual	ADJ
ejpam-6178	227	13	computations	computation	NOUN
ejpam-6178	227	14	,	,	PUNCT
ejpam-6178	227	15	φ	φ	PROPN
ejpam-6178	227	16	is	be	AUX
ejpam-6178	227	17	an	an	DET
ejpam-6178	227	18	open	open	ADJ
ejpam-6178	227	19	mapping	mapping	NOUN
ejpam-6178	227	20	.	.	PUNCT
ejpam-6178	228	1	the	the	DET
ejpam-6178	228	2	next	next	ADJ
ejpam-6178	228	3	result	result	NOUN
ejpam-6178	228	4	establishes	establish	VERB
ejpam-6178	228	5	the	the	DET
ejpam-6178	228	6	tdb	tdb	PROPN
ejpam-6178	228	7	-	-	PUNCT
ejpam-6178	228	8	homomorphisms	homomorphism	NOUN
ejpam-6178	228	9	and	and	CCONJ
ejpam-6178	228	10	some	some	PRON
ejpam-6178	228	11	of	of	ADP
ejpam-6178	228	12	its	its	PRON
ejpam-6178	228	13	properties	property	NOUN
ejpam-6178	228	14	with	with	ADP
ejpam-6178	228	15	the	the	DET
ejpam-6178	228	16	use	use	NOUN
ejpam-6178	228	17	of	of	ADP
ejpam-6178	228	18	some	some	DET
ejpam-6178	228	19	properties	property	NOUN
ejpam-6178	228	20	of	of	ADP
ejpam-6178	228	21	the	the	DET
ejpam-6178	228	22	natural	natural	ADJ
ejpam-6178	228	23	db	db	NOUN
ejpam-6178	228	24	-	-	PUNCT
ejpam-6178	228	25	homomorphism	homomorphism	NOUN
ejpam-6178	228	26	.	.	PUNCT
ejpam-6178	229	1	theorem	theorem	ADJ
ejpam-6178	229	2	14	14	NUM
ejpam-6178	229	3	.	.	PUNCT
ejpam-6178	230	1	let	let	VERB
ejpam-6178	230	2	(	(	PUNCT
ejpam-6178	230	3	x	x	NOUN
ejpam-6178	230	4	,	,	PUNCT
ejpam-6178	230	5	◦	◦	NOUN
ejpam-6178	230	6	,	,	PUNCT
ejpam-6178	230	7	τ	τ	X
ejpam-6178	230	8	)	)	PUNCT
ejpam-6178	230	9	be	be	VERB
ejpam-6178	230	10	a	a	DET
ejpam-6178	230	11	tdb	tdb	NOUN
ejpam-6178	230	12	-	-	NOUN
ejpam-6178	230	13	algebra	algebra	PROPN
ejpam-6178	230	14	and	and	CCONJ
ejpam-6178	230	15	s	s	NOUN
ejpam-6178	230	16	⊆	⊆	NUM
ejpam-6178	230	17	x.	x.	NOUN
ejpam-6178	230	18	then	then	ADV
ejpam-6178	230	19	the	the	DET
ejpam-6178	230	20	following	follow	VERB
ejpam-6178	230	21	statements	statement	NOUN
ejpam-6178	230	22	hold	hold	VERB
ejpam-6178	230	23	:	:	PUNCT
ejpam-6178	230	24	(	(	PUNCT
ejpam-6178	230	25	i	i	NOUN
ejpam-6178	230	26	)	)	PUNCT
ejpam-6178	230	27	if	if	SCONJ
ejpam-6178	230	28	the	the	DET
ejpam-6178	230	29	the	the	DET
ejpam-6178	230	30	natural	natural	ADJ
ejpam-6178	230	31	db	db	NOUN
ejpam-6178	230	32	-	-	PUNCT
ejpam-6178	230	33	homomorphism	homomorphism	NOUN
ejpam-6178	230	34	φ	φ	PROPN
ejpam-6178	230	35	is	be	AUX
ejpam-6178	230	36	open	open	ADJ
ejpam-6178	230	37	from	from	ADP
ejpam-6178	230	38	x	x	PUNCT
ejpam-6178	230	39	onto	onto	ADP
ejpam-6178	230	40	x	x	PROPN
ejpam-6178	230	41	/	/	SYM
ejpam-6178	230	42	s	s	PROPN
ejpam-6178	230	43	,	,	PUNCT
ejpam-6178	230	44	then	then	ADV
ejpam-6178	230	45	φ	φ	PROPN
ejpam-6178	230	46	is	be	AUX
ejpam-6178	230	47	a	a	DET
ejpam-6178	230	48	tdb	tdb	PROPN
ejpam-6178	230	49	-	-	NOUN
ejpam-6178	230	50	homomorphism	homomorphism	NOUN
ejpam-6178	230	51	;	;	PUNCT
ejpam-6178	230	52	and	and	CCONJ
ejpam-6178	230	53	(	(	PUNCT
ejpam-6178	230	54	ii	ii	NOUN
ejpam-6178	230	55	)	)	PUNCT
ejpam-6178	230	56	if	if	SCONJ
ejpam-6178	230	57	s	s	NOUN
ejpam-6178	230	58	is	be	AUX
ejpam-6178	230	59	open	open	ADJ
ejpam-6178	230	60	,	,	PUNCT
ejpam-6178	230	61	then	then	ADV
ejpam-6178	230	62	the	the	DET
ejpam-6178	230	63	natural	natural	ADJ
ejpam-6178	230	64	db	db	NOUN
ejpam-6178	230	65	-	-	PUNCT
ejpam-6178	230	66	homomorphism	homomorphism	NOUN
ejpam-6178	230	67	φ	φ	PROPN
ejpam-6178	230	68	is	be	AUX
ejpam-6178	230	69	an	an	DET
ejpam-6178	230	70	open	open	ADJ
ejpam-6178	230	71	tdb	tdb	NOUN
ejpam-6178	230	72	-	-	NOUN
ejpam-6178	230	73	homomorphism	homomorphism	NOUN
ejpam-6178	230	74	.	.	PUNCT
ejpam-6178	231	1	proof	proof	NOUN
ejpam-6178	231	2	.	.	PUNCT
ejpam-6178	232	1	clearly	clearly	ADV
ejpam-6178	232	2	,	,	PUNCT
ejpam-6178	232	3	φ	φ	PROPN
ejpam-6178	232	4	is	be	AUX
ejpam-6178	232	5	a	a	DET
ejpam-6178	232	6	db	db	NOUN
ejpam-6178	232	7	-	-	PUNCT
ejpam-6178	232	8	homomorphism	homomorphism	NOUN
ejpam-6178	232	9	from	from	ADP
ejpam-6178	232	10	x	x	PRON
ejpam-6178	232	11	to	to	ADP
ejpam-6178	232	12	x	x	X
ejpam-6178	232	13	/	/	SYM
ejpam-6178	232	14	s	s	X
ejpam-6178	232	15	and	and	CCONJ
ejpam-6178	232	16	by	by	ADP
ejpam-6178	232	17	theorem	theorem	NOUN
ejpam-6178	232	18	11	11	NUM
ejpam-6178	232	19	,	,	PUNCT
ejpam-6178	232	20	φ	φ	PROPN
ejpam-6178	232	21	is	be	AUX
ejpam-6178	232	22	continuous	continuous	ADJ
ejpam-6178	232	23	.	.	PUNCT
ejpam-6178	233	1	(	(	PUNCT
ejpam-6178	233	2	i	i	NOUN
ejpam-6178	233	3	)	)	PUNCT
ejpam-6178	233	4	note	note	VERB
ejpam-6178	233	5	that	that	SCONJ
ejpam-6178	233	6	x	x	X
ejpam-6178	233	7	/	/	SYM
ejpam-6178	233	8	s	s	X
ejpam-6178	233	9	is	be	AUX
ejpam-6178	233	10	a	a	DET
ejpam-6178	233	11	tdb	tdb	NOUN
ejpam-6178	233	12	-	-	NOUN
ejpam-6178	233	13	algebra	algebra	NOUN
ejpam-6178	233	14	by	by	ADP
ejpam-6178	233	15	theorem	theorem	NOUN
ejpam-6178	233	16	12	12	NUM
ejpam-6178	233	17	.	.	PUNCT
ejpam-6178	234	1	by	by	ADP
ejpam-6178	234	2	definition	definition	NOUN
ejpam-6178	234	3	12	12	NUM
ejpam-6178	234	4	,	,	PUNCT
ejpam-6178	234	5	it	it	PRON
ejpam-6178	234	6	follows	follow	VERB
ejpam-6178	234	7	that	that	SCONJ
ejpam-6178	234	8	φ	φ	PROPN
ejpam-6178	234	9	is	be	AUX
ejpam-6178	234	10	a	a	DET
ejpam-6178	234	11	tdb	tdb	PROPN
ejpam-6178	234	12	-	-	NOUN
ejpam-6178	234	13	homomorphism	homomorphism	NOUN
ejpam-6178	234	14	.	.	PUNCT
ejpam-6178	235	1	(	(	PUNCT
ejpam-6178	235	2	ii	ii	NOUN
ejpam-6178	235	3	)	)	PUNCT
ejpam-6178	235	4	suppose	suppose	VERB
ejpam-6178	235	5	s	s	NOUN
ejpam-6178	235	6	is	be	AUX
ejpam-6178	235	7	open	open	ADJ
ejpam-6178	235	8	.	.	PUNCT
ejpam-6178	236	1	then	then	ADV
ejpam-6178	236	2	by	by	ADP
ejpam-6178	236	3	theorem	theorem	ADJ
ejpam-6178	236	4	13	13	NUM
ejpam-6178	236	5	and	and	CCONJ
ejpam-6178	236	6	corollary	corollary	ADJ
ejpam-6178	236	7	1	1	NUM
ejpam-6178	236	8	,	,	PUNCT
ejpam-6178	236	9	φ	φ	PROPN
ejpam-6178	236	10	is	be	AUX
ejpam-6178	236	11	an	an	DET
ejpam-6178	236	12	open	open	ADJ
ejpam-6178	236	13	mapping	mapping	NOUN
ejpam-6178	236	14	and	and	CCONJ
ejpam-6178	236	15	x	x	NOUN
ejpam-6178	236	16	/	/	SYM
ejpam-6178	236	17	s	s	X
ejpam-6178	236	18	is	be	AUX
ejpam-6178	236	19	a	a	DET
ejpam-6178	236	20	tdb	tdb	NOUN
ejpam-6178	236	21	-	-	NOUN
ejpam-6178	236	22	algebra	algebra	NOUN
ejpam-6178	236	23	,	,	PUNCT
ejpam-6178	236	24	respectively	respectively	ADV
ejpam-6178	236	25	.	.	PUNCT
ejpam-6178	237	1	hence	hence	ADV
ejpam-6178	237	2	,	,	PUNCT
ejpam-6178	237	3	φ	φ	PROPN
ejpam-6178	237	4	is	be	AUX
ejpam-6178	237	5	an	an	DET
ejpam-6178	237	6	open	open	ADJ
ejpam-6178	237	7	tdb	tdb	NOUN
ejpam-6178	237	8	-	-	NOUN
ejpam-6178	237	9	homomorphism	homomorphism	NOUN
ejpam-6178	237	10	.	.	PUNCT
ejpam-6178	238	1	the	the	DET
ejpam-6178	238	2	next	next	ADJ
ejpam-6178	238	3	theorem	theorem	NOUN
ejpam-6178	238	4	establishes	establish	VERB
ejpam-6178	238	5	the	the	DET
ejpam-6178	238	6	topological	topological	ADJ
ejpam-6178	238	7	dual	dual	PROPN
ejpam-6178	238	8	b	b	NOUN
ejpam-6178	238	9	-	-	PUNCT
ejpam-6178	238	10	homomorphism	homomorphism	NOUN
ejpam-6178	238	11	using	use	VERB
ejpam-6178	238	12	two	two	NUM
ejpam-6178	238	13	natural	natural	ADJ
ejpam-6178	238	14	db	db	NOUN
ejpam-6178	238	15	-	-	PUNCT
ejpam-6178	238	16	homomorphism	homomorphism	NOUN
ejpam-6178	238	17	.	.	PUNCT
ejpam-6178	239	1	r.	r.	PROPN
ejpam-6178	239	2	nuñez	nuñez	PROPN
ejpam-6178	239	3	,	,	PUNCT
ejpam-6178	239	4	k.	k.	PROPN
ejpam-6178	239	5	b.	b.	PROPN
ejpam-6178	239	6	fuentes	fuentes	PROPN
ejpam-6178	239	7	/	/	SYM
ejpam-6178	239	8	eur	eur	PROPN
ejpam-6178	239	9	.	.	PUNCT
ejpam-6178	240	1	j.	j.	PROPN
ejpam-6178	240	2	pure	pure	PROPN
ejpam-6178	240	3	appl	appl	PROPN
ejpam-6178	240	4	.	.	PROPN
ejpam-6178	240	5	math	math	PROPN
ejpam-6178	240	6	,	,	PUNCT
ejpam-6178	240	7	18	18	NUM
ejpam-6178	240	8	(	(	PUNCT
ejpam-6178	240	9	4	4	NUM
ejpam-6178	240	10	)	)	PUNCT
ejpam-6178	240	11	(	(	PUNCT
ejpam-6178	240	12	2025	2025	NUM
ejpam-6178	240	13	)	)	PUNCT
ejpam-6178	240	14	,	,	PUNCT
ejpam-6178	240	15	6178	6178	NUM
ejpam-6178	240	16	8	8	NUM
ejpam-6178	240	17	of	of	ADP
ejpam-6178	240	18	15	15	NUM
ejpam-6178	240	19	theorem	theorem	NOUN
ejpam-6178	240	20	15	15	NUM
ejpam-6178	240	21	.	.	PUNCT
ejpam-6178	241	1	let	let	VERB
ejpam-6178	241	2	s	s	PRON
ejpam-6178	241	3	and	and	CCONJ
ejpam-6178	241	4	j	j	PROPN
ejpam-6178	241	5	be	be	AUX
ejpam-6178	241	6	normal	normal	ADJ
ejpam-6178	241	7	db	db	NOUN
ejpam-6178	241	8	-	-	PUNCT
ejpam-6178	241	9	subalgebras	subalgebras	PROPN
ejpam-6178	241	10	of	of	ADP
ejpam-6178	241	11	a	a	DET
ejpam-6178	241	12	tdb	tdb	NOUN
ejpam-6178	241	13	-	-	NOUN
ejpam-6178	241	14	algebra	algebra	NOUN
ejpam-6178	241	15	(	(	PUNCT
ejpam-6178	241	16	x	x	X
ejpam-6178	241	17	,	,	PUNCT
ejpam-6178	241	18	◦	◦	NOUN
ejpam-6178	241	19	,	,	PUNCT
ejpam-6178	241	20	τ	τ	X
ejpam-6178	241	21	)	)	PUNCT
ejpam-6178	241	22	such	such	ADJ
ejpam-6178	241	23	that	that	PRON
ejpam-6178	241	24	s	s	PROPN
ejpam-6178	242	1	⊂	⊂	PROPN
ejpam-6178	242	2	j	j	PROPN
ejpam-6178	242	3	.	.	PUNCT
ejpam-6178	243	1	define	define	VERB
ejpam-6178	243	2	a	a	DET
ejpam-6178	243	3	map	map	NOUN
ejpam-6178	243	4	f	f	NOUN
ejpam-6178	243	5	from	from	ADP
ejpam-6178	243	6	(	(	PUNCT
ejpam-6178	243	7	x	x	X
ejpam-6178	243	8	/	/	SYM
ejpam-6178	243	9	s	s	PROPN
ejpam-6178	243	10	,	,	PUNCT
ejpam-6178	243	11	∗	∗	NOUN
ejpam-6178	243	12	,	,	PUNCT
ejpam-6178	243	13	τs	τs	NOUN
ejpam-6178	243	14	)	)	PUNCT
ejpam-6178	243	15	to	to	ADP
ejpam-6178	243	16	(	(	PUNCT
ejpam-6178	243	17	x	x	SYM
ejpam-6178	243	18	/	/	SYM
ejpam-6178	243	19	j	j	PROPN
ejpam-6178	243	20	,	,	PUNCT
ejpam-6178	243	21	∗′	∗′	PROPN
ejpam-6178	243	22	,	,	PUNCT
ejpam-6178	243	23	τj	τj	NOUN
ejpam-6178	243	24	)	)	PUNCT
ejpam-6178	243	25	by	by	ADP
ejpam-6178	243	26	f([x]s	f([x]s	ADJ
ejpam-6178	243	27	)	)	PUNCT
ejpam-6178	243	28	=	=	PUNCT
ejpam-6178	244	1	[	[	X
ejpam-6178	244	2	x]j	x]j	X
ejpam-6178	244	3	for	for	ADP
ejpam-6178	244	4	all	all	PRON
ejpam-6178	244	5	[	[	X
ejpam-6178	244	6	x]s	x]s	PROPN
ejpam-6178	244	7	∈	∈	PROPN
ejpam-6178	244	8	x	x	X
ejpam-6178	244	9	/	/	SYM
ejpam-6178	244	10	s.	s.	PROPN
ejpam-6178	244	11	if	if	SCONJ
ejpam-6178	244	12	the	the	DET
ejpam-6178	244	13	natural	natural	ADJ
ejpam-6178	244	14	db	db	NOUN
ejpam-6178	244	15	-	-	PUNCT
ejpam-6178	244	16	homomorphism	homomorphism	NOUN
ejpam-6178	244	17	φ	φ	NOUN
ejpam-6178	244	18	from	from	ADP
ejpam-6178	244	19	x	x	PRON
ejpam-6178	244	20	onto	onto	ADP
ejpam-6178	244	21	x	x	PROPN
ejpam-6178	244	22	/	/	SYM
ejpam-6178	244	23	s	s	X
ejpam-6178	244	24	and	and	CCONJ
ejpam-6178	244	25	the	the	DET
ejpam-6178	244	26	natural	natural	ADJ
ejpam-6178	244	27	dbhomomorphism	dbhomomorphism	NOUN
ejpam-6178	244	28	ψ	ψ	NOUN
ejpam-6178	244	29	from	from	ADP
ejpam-6178	244	30	x	x	PUNCT
ejpam-6178	244	31	onto	onto	ADP
ejpam-6178	244	32	x	x	SYM
ejpam-6178	244	33	/	/	SYM
ejpam-6178	244	34	j	j	PROPN
ejpam-6178	244	35	are	be	AUX
ejpam-6178	244	36	open	open	ADJ
ejpam-6178	244	37	mappings	mapping	NOUN
ejpam-6178	244	38	,	,	PUNCT
ejpam-6178	244	39	then	then	ADV
ejpam-6178	244	40	f	f	PROPN
ejpam-6178	244	41	is	be	AUX
ejpam-6178	244	42	a	a	DET
ejpam-6178	244	43	tdb	tdb	PROPN
ejpam-6178	244	44	-	-	NOUN
ejpam-6178	244	45	homomorphism	homomorphism	NOUN
ejpam-6178	244	46	.	.	PUNCT
ejpam-6178	245	1	proof	proof	NOUN
ejpam-6178	245	2	.	.	PUNCT
ejpam-6178	246	1	claim	claim	VERB
ejpam-6178	246	2	1	1	NUM
ejpam-6178	246	3	:	:	PUNCT
ejpam-6178	246	4	f	f	PROPN
ejpam-6178	246	5	is	be	AUX
ejpam-6178	246	6	well	well	ADV
ejpam-6178	246	7	-	-	PUNCT
ejpam-6178	246	8	defined	define	VERB
ejpam-6178	246	9	.	.	PUNCT
ejpam-6178	247	1	let	let	VERB
ejpam-6178	247	2	[	[	X
ejpam-6178	247	3	x]s	x]s	PROPN
ejpam-6178	247	4	,	,	PUNCT
ejpam-6178	247	5	[	[	X
ejpam-6178	247	6	y]s	y]s	X
ejpam-6178	247	7	∈	∈	NOUN
ejpam-6178	247	8	x	x	PRON
ejpam-6178	247	9	/	/	SYM
ejpam-6178	247	10	s	s	VERB
ejpam-6178	247	11	such	such	ADJ
ejpam-6178	247	12	that	that	SCONJ
ejpam-6178	248	1	[	[	X
ejpam-6178	248	2	x]s	x]s	NOUN
ejpam-6178	248	3	=	=	PUNCT
ejpam-6178	249	1	[	[	X
ejpam-6178	249	2	y]s	y]s	X
ejpam-6178	249	3	.	.	PUNCT
ejpam-6178	250	1	then	then	ADV
ejpam-6178	250	2	x	x	SYM
ejpam-6178	250	3	∼s	∼s	PUNCT
ejpam-6178	250	4	y	y	PROPN
ejpam-6178	250	5	by	by	ADP
ejpam-6178	250	6	lemma	lemma	PROPN
ejpam-6178	250	7	1	1	NUM
ejpam-6178	250	8	.	.	PUNCT
ejpam-6178	251	1	it	it	PRON
ejpam-6178	251	2	follows	follow	VERB
ejpam-6178	251	3	that	that	SCONJ
ejpam-6178	251	4	x	x	PUNCT
ejpam-6178	252	1	◦	◦	NOUN
ejpam-6178	252	2	y	y	PROPN
ejpam-6178	252	3	,	,	PUNCT
ejpam-6178	252	4	y	y	PROPN
ejpam-6178	252	5	◦	◦	NOUN
ejpam-6178	252	6	x	x	SYM
ejpam-6178	252	7	∈	∈	PROPN
ejpam-6178	252	8	s.	s.	PROPN
ejpam-6178	252	9	since	since	SCONJ
ejpam-6178	252	10	s	s	PROPN
ejpam-6178	252	11	⊆	⊆	NUM
ejpam-6178	252	12	j	j	NOUN
ejpam-6178	252	13	,	,	PUNCT
ejpam-6178	252	14	x	x	PUNCT
ejpam-6178	252	15	◦	◦	NOUN
ejpam-6178	252	16	y	y	PROPN
ejpam-6178	252	17	,	,	PUNCT
ejpam-6178	252	18	y	y	PROPN
ejpam-6178	252	19	◦	◦	NOUN
ejpam-6178	252	20	x	x	PUNCT
ejpam-6178	252	21	∈	∈	PROPN
ejpam-6178	252	22	j	j	NOUN
ejpam-6178	252	23	which	which	PRON
ejpam-6178	252	24	implies	imply	VERB
ejpam-6178	252	25	that	that	SCONJ
ejpam-6178	252	26	x	x	X
ejpam-6178	252	27	∼j	∼j	PROPN
ejpam-6178	252	28	y.	y.	NOUN
ejpam-6178	252	29	hence	hence	ADV
ejpam-6178	252	30	,	,	PUNCT
ejpam-6178	253	1	[	[	X
ejpam-6178	253	2	x]j	x]j	X
ejpam-6178	253	3	=	=	PUNCT
ejpam-6178	254	1	[	[	X
ejpam-6178	254	2	y]j	y]j	NOUN
ejpam-6178	254	3	.	.	PUNCT
ejpam-6178	255	1	consequently	consequently	ADV
ejpam-6178	255	2	,	,	PUNCT
ejpam-6178	255	3	f([x]s	f([x]s	PROPN
ejpam-6178	255	4	)	)	PUNCT
ejpam-6178	255	5	=	=	SYM
ejpam-6178	255	6	f([y]s	f([y]	NOUN
ejpam-6178	255	7	)	)	PUNCT
ejpam-6178	255	8	.	.	PUNCT
ejpam-6178	256	1	therefore	therefore	ADV
ejpam-6178	256	2	,	,	PUNCT
ejpam-6178	256	3	f	f	PROPN
ejpam-6178	256	4	is	be	AUX
ejpam-6178	256	5	well	well	ADV
ejpam-6178	256	6	-	-	PUNCT
ejpam-6178	256	7	defined	define	VERB
ejpam-6178	256	8	.	.	PUNCT
ejpam-6178	257	1	claim	claim	NOUN
ejpam-6178	257	2	2	2	NUM
ejpam-6178	257	3	:	:	PUNCT
ejpam-6178	257	4	f	f	PROPN
ejpam-6178	257	5	is	be	AUX
ejpam-6178	257	6	db	db	PROPN
ejpam-6178	257	7	-	-	PUNCT
ejpam-6178	257	8	homomorphism	homomorphism	NOUN
ejpam-6178	257	9	.	.	PUNCT
ejpam-6178	258	1	let	let	VERB
ejpam-6178	258	2	[	[	X
ejpam-6178	258	3	x]s	x]s	PROPN
ejpam-6178	258	4	,	,	PUNCT
ejpam-6178	258	5	[	[	X
ejpam-6178	258	6	y]s	y]s	X
ejpam-6178	258	7	∈	∈	PROPN
ejpam-6178	258	8	x	x	PRON
ejpam-6178	258	9	/	/	SYM
ejpam-6178	258	10	s.	s.	PROPN
ejpam-6178	258	11	then	then	ADV
ejpam-6178	258	12	f([x]s	f([x]s	VERB
ejpam-6178	258	13	∗[y]s	∗[y]	NOUN
ejpam-6178	258	14	)	)	PUNCT
ejpam-6178	258	15	=	=	SYM
ejpam-6178	259	1	f([x	f([x	NOUN
ejpam-6178	259	2	◦	◦	NOUN
ejpam-6178	259	3	y]s	y]s	NUM
ejpam-6178	259	4	)	)	PUNCT
ejpam-6178	260	1	=	=	PUNCT
ejpam-6178	261	1	[	[	X
ejpam-6178	261	2	x	x	PART
ejpam-6178	261	3	◦	◦	NOUN
ejpam-6178	261	4	y]j	y]j	NOUN
ejpam-6178	261	5	=	=	SYM
ejpam-6178	262	1	[	[	X
ejpam-6178	262	2	x]j	x]j	X
ejpam-6178	262	3	∗′	∗′	ADJ
ejpam-6178	262	4	[	[	X
ejpam-6178	262	5	y]j	y]j	NOUN
ejpam-6178	262	6	=	=	PUNCT
ejpam-6178	262	7	f([x]s	f([x]s	ADJ
ejpam-6178	262	8	)	)	PUNCT
ejpam-6178	262	9	∗′	∗′	PROPN
ejpam-6178	262	10	f([y]s	f([y]s	NOUN
ejpam-6178	262	11	)	)	PUNCT
ejpam-6178	262	12	.	.	PUNCT
ejpam-6178	263	1	therefore	therefore	ADV
ejpam-6178	263	2	,	,	PUNCT
ejpam-6178	263	3	f	f	PROPN
ejpam-6178	263	4	is	be	AUX
ejpam-6178	263	5	db	db	PROPN
ejpam-6178	263	6	-	-	PUNCT
ejpam-6178	263	7	homomorphism	homomorphism	NOUN
ejpam-6178	263	8	.	.	PUNCT
ejpam-6178	264	1	claim	claim	NOUN
ejpam-6178	264	2	3	3	NUM
ejpam-6178	264	3	:	:	PUNCT
ejpam-6178	264	4	f	f	PROPN
ejpam-6178	264	5	is	be	AUX
ejpam-6178	264	6	continuous	continuous	ADJ
ejpam-6178	264	7	.	.	PUNCT
ejpam-6178	264	8	suppose	suppose	VERB
ejpam-6178	264	9	that	that	SCONJ
ejpam-6178	264	10	φ	φ	PROPN
ejpam-6178	264	11	and	and	CCONJ
ejpam-6178	264	12	ψ	ψ	NOUN
ejpam-6178	264	13	are	be	AUX
ejpam-6178	264	14	open	open	ADJ
ejpam-6178	264	15	mappings	mapping	NOUN
ejpam-6178	264	16	.	.	PUNCT
ejpam-6178	265	1	by	by	ADP
ejpam-6178	265	2	theorem	theorem	NOUN
ejpam-6178	265	3	12	12	NUM
ejpam-6178	265	4	,	,	PUNCT
ejpam-6178	265	5	x	x	X
ejpam-6178	265	6	/	/	SYM
ejpam-6178	265	7	s	s	X
ejpam-6178	265	8	and	and	CCONJ
ejpam-6178	265	9	x	x	X
ejpam-6178	265	10	/	/	SYM
ejpam-6178	265	11	j	j	PROPN
ejpam-6178	265	12	are	be	AUX
ejpam-6178	265	13	tdb	tdb	PROPN
ejpam-6178	265	14	-	-	PUNCT
ejpam-6178	265	15	algebras	algebras	X
ejpam-6178	265	16	.	.	PUNCT
ejpam-6178	266	1	let	let	VERB
ejpam-6178	266	2	u	u	PRON
ejpam-6178	266	3	be	be	AUX
ejpam-6178	266	4	open	open	ADJ
ejpam-6178	266	5	in	in	ADP
ejpam-6178	266	6	x	x	PROPN
ejpam-6178	266	7	/	/	SYM
ejpam-6178	266	8	j	j	PROPN
ejpam-6178	266	9	and	and	CCONJ
ejpam-6178	266	10	[	[	X
ejpam-6178	266	11	x]s	x]s	PROPN
ejpam-6178	266	12	∈	∈	PROPN
ejpam-6178	266	13	f−1(u	f−1(u	PROPN
ejpam-6178	266	14	)	)	PUNCT
ejpam-6178	266	15	.	.	PUNCT
ejpam-6178	267	1	then	then	ADV
ejpam-6178	267	2	f([x]s	f([x]s	X
ejpam-6178	267	3	)	)	PUNCT
ejpam-6178	267	4	∈	∈	PROPN
ejpam-6178	267	5	f(f−1(u	f(f−1(u	PROPN
ejpam-6178	267	6	)	)	PUNCT
ejpam-6178	267	7	)	)	PUNCT
ejpam-6178	268	1	⊆	⊆	NUM
ejpam-6178	268	2	u	u	NOUN
ejpam-6178	268	3	by	by	ADP
ejpam-6178	268	4	theorem	theorem	ADJ
ejpam-6178	268	5	9	9	NUM
ejpam-6178	268	6	(	(	PUNCT
ejpam-6178	268	7	ii	ii	NOUN
ejpam-6178	268	8	)	)	PUNCT
ejpam-6178	268	9	.	.	PUNCT
ejpam-6178	269	1	it	it	PRON
ejpam-6178	269	2	follows	follow	VERB
ejpam-6178	269	3	that	that	SCONJ
ejpam-6178	269	4	[	[	X
ejpam-6178	269	5	x]j	x]j	X
ejpam-6178	269	6	=	=	SYM
ejpam-6178	269	7	f([x]s	f([x]s	ADJ
ejpam-6178	269	8	)	)	PUNCT
ejpam-6178	269	9	∈	∈	PROPN
ejpam-6178	269	10	u	u	NOUN
ejpam-6178	269	11	.	.	PUNCT
ejpam-6178	270	1	since	since	SCONJ
ejpam-6178	270	2	u	u	NOUN
ejpam-6178	270	3	is	be	AUX
ejpam-6178	270	4	open	open	ADJ
ejpam-6178	270	5	,	,	PUNCT
ejpam-6178	270	6	there	there	PRON
ejpam-6178	270	7	exists	exist	VERB
ejpam-6178	270	8	a	a	DET
ejpam-6178	270	9	neighborhood	neighborhood	NOUN
ejpam-6178	270	10	w	w	NOUN
ejpam-6178	270	11	of	of	ADP
ejpam-6178	270	12	f([x]s	f([x]s	ADJ
ejpam-6178	270	13	)	)	PUNCT
ejpam-6178	270	14	=	=	PUNCT
ejpam-6178	271	1	[	[	X
ejpam-6178	271	2	x]j	x]j	X
ejpam-6178	271	3	in	in	ADP
ejpam-6178	271	4	x	x	PROPN
ejpam-6178	271	5	/	/	SYM
ejpam-6178	271	6	j	j	PROPN
ejpam-6178	271	7	such	such	ADJ
ejpam-6178	271	8	that	that	SCONJ
ejpam-6178	271	9	w	w	PROPN
ejpam-6178	271	10	⊆	⊆	NUM
ejpam-6178	271	11	u	u	NOUN
ejpam-6178	271	12	by	by	ADP
ejpam-6178	271	13	remark	remark	NOUN
ejpam-6178	271	14	2	2	NUM
ejpam-6178	271	15	.	.	PUNCT
ejpam-6178	272	1	moreover	moreover	ADV
ejpam-6178	272	2	,	,	PUNCT
ejpam-6178	272	3	[	[	X
ejpam-6178	272	4	x]s	x]s	PROPN
ejpam-6178	272	5	∈	∈	PROPN
ejpam-6178	272	6	f−1(w	f−1(w	PROPN
ejpam-6178	272	7	)	)	PUNCT
ejpam-6178	272	8	.	.	PUNCT
ejpam-6178	273	1	now	now	ADV
ejpam-6178	273	2	f−1(w	f−1(w	ADV
ejpam-6178	273	3	)	)	PUNCT
ejpam-6178	273	4	=	=	PUNCT
ejpam-6178	274	1	{	{	PUNCT
ejpam-6178	274	2	[	[	X
ejpam-6178	274	3	x′]s	x′]s	X
ejpam-6178	274	4	∈	∈	NOUN
ejpam-6178	274	5	x	x	X
ejpam-6178	274	6	/	/	SYM
ejpam-6178	274	7	s	s	PART
ejpam-6178	274	8	|	|	ADV
ejpam-6178	274	9	f([x′]s	f([x′]s	ADJ
ejpam-6178	274	10	)	)	PUNCT
ejpam-6178	274	11	=	=	PUNCT
ejpam-6178	275	1	[	[	X
ejpam-6178	275	2	x′]j	x′]j	X
ejpam-6178	275	3	∈	∈	PROPN
ejpam-6178	275	4	w	w	PROPN
ejpam-6178	275	5	}	}	PUNCT
ejpam-6178	275	6	=	=	PUNCT
ejpam-6178	275	7	{	{	PUNCT
ejpam-6178	276	1	[	[	X
ejpam-6178	276	2	x′]s	x′]s	X
ejpam-6178	276	3	∈	∈	NOUN
ejpam-6178	276	4	x	x	X
ejpam-6178	276	5	/	/	SYM
ejpam-6178	276	6	s	s	PART
ejpam-6178	276	7	|	|	NOUN
ejpam-6178	276	8	ψ(x′	ψ(x′	NUM
ejpam-6178	276	9	)	)	PUNCT
ejpam-6178	277	1	=	=	PUNCT
ejpam-6178	278	1	[	[	X
ejpam-6178	278	2	x′]j	x′]j	X
ejpam-6178	278	3	∈	∈	PROPN
ejpam-6178	278	4	w	w	PROPN
ejpam-6178	278	5	}	}	PUNCT
ejpam-6178	278	6	=	=	PUNCT
ejpam-6178	278	7	{	{	PUNCT
ejpam-6178	278	8	[	[	X
ejpam-6178	278	9	x′]s	x′]s	X
ejpam-6178	278	10	∈	∈	NOUN
ejpam-6178	278	11	x	x	X
ejpam-6178	278	12	/	/	SYM
ejpam-6178	278	13	s	s	VERB
ejpam-6178	278	14	|	|	ADV
ejpam-6178	278	15	x′	x′	PROPN
ejpam-6178	278	16	∈	∈	PROPN
ejpam-6178	278	17	ψ−1(w	ψ−1(w	NOUN
ejpam-6178	278	18	)	)	PUNCT
ejpam-6178	278	19	}	}	PUNCT
ejpam-6178	278	20	=	=	SYM
ejpam-6178	278	21	{	{	PUNCT
ejpam-6178	278	22	φ(x′	φ(x′	NOUN
ejpam-6178	278	23	)	)	PUNCT
ejpam-6178	278	24	∈	∈	NOUN
ejpam-6178	278	25	x	x	X
ejpam-6178	278	26	/	/	SYM
ejpam-6178	278	27	s	s	VERB
ejpam-6178	278	28	|	|	ADV
ejpam-6178	278	29	x′	x′	PROPN
ejpam-6178	278	30	∈	∈	PROPN
ejpam-6178	278	31	ψ−1(w	ψ−1(w	NOUN
ejpam-6178	278	32	)	)	PUNCT
ejpam-6178	278	33	}	}	PUNCT
ejpam-6178	278	34	=	=	PUNCT
ejpam-6178	278	35	φ(ψ−1(w	φ(ψ−1(w	PROPN
ejpam-6178	278	36	)	)	PUNCT
ejpam-6178	278	37	)	)	PUNCT
ejpam-6178	278	38	since	since	SCONJ
ejpam-6178	278	39	w	w	NOUN
ejpam-6178	278	40	is	be	AUX
ejpam-6178	278	41	open	open	ADJ
ejpam-6178	278	42	in	in	ADP
ejpam-6178	278	43	x	x	PROPN
ejpam-6178	278	44	/	/	SYM
ejpam-6178	278	45	j	j	PROPN
ejpam-6178	278	46	and	and	CCONJ
ejpam-6178	278	47	ψ	ψ	PROPN
ejpam-6178	278	48	is	be	AUX
ejpam-6178	278	49	continuous	continuous	ADJ
ejpam-6178	278	50	by	by	ADP
ejpam-6178	278	51	theorem	theorem	NOUN
ejpam-6178	278	52	11	11	NUM
ejpam-6178	278	53	,	,	PUNCT
ejpam-6178	278	54	then	then	ADV
ejpam-6178	278	55	ψ−1(w	ψ−1(w	PROPN
ejpam-6178	278	56	)	)	PUNCT
ejpam-6178	278	57	is	be	AUX
ejpam-6178	278	58	open	open	ADJ
ejpam-6178	278	59	in	in	ADP
ejpam-6178	278	60	x.	x.	NOUN
ejpam-6178	278	61	since	since	SCONJ
ejpam-6178	278	62	φ	φ	PROPN
ejpam-6178	278	63	is	be	AUX
ejpam-6178	278	64	an	an	DET
ejpam-6178	278	65	open	open	ADJ
ejpam-6178	278	66	mapping	mapping	NOUN
ejpam-6178	278	67	,	,	PUNCT
ejpam-6178	278	68	φ(ψ−1(w	φ(ψ−1(w	PROPN
ejpam-6178	278	69	)	)	PUNCT
ejpam-6178	278	70	)	)	PUNCT
ejpam-6178	279	1	=	=	SYM
ejpam-6178	279	2	f−1(w	f−1(w	ADV
ejpam-6178	279	3	)	)	PUNCT
ejpam-6178	279	4	is	be	AUX
ejpam-6178	279	5	open	open	ADJ
ejpam-6178	279	6	in	in	ADP
ejpam-6178	279	7	x	x	X
ejpam-6178	279	8	/	/	SYM
ejpam-6178	279	9	s.	s.	PROPN
ejpam-6178	279	10	moreover	moreover	ADV
ejpam-6178	279	11	,	,	PUNCT
ejpam-6178	279	12	since	since	SCONJ
ejpam-6178	279	13	w	w	PROPN
ejpam-6178	279	14	⊆	⊆	NUM
ejpam-6178	279	15	u	u	NOUN
ejpam-6178	279	16	,	,	PUNCT
ejpam-6178	279	17	it	it	PRON
ejpam-6178	279	18	follows	follow	VERB
ejpam-6178	279	19	that	that	SCONJ
ejpam-6178	279	20	f−1(w	f−1(w	PROPN
ejpam-6178	279	21	)	)	PUNCT
ejpam-6178	279	22	⊆	⊆	NUM
ejpam-6178	279	23	f−1(u	f−1(u	NOUN
ejpam-6178	279	24	)	)	PUNCT
ejpam-6178	279	25	by	by	ADP
ejpam-6178	279	26	theorem	theorem	ADJ
ejpam-6178	279	27	9	9	NUM
ejpam-6178	279	28	(	(	PUNCT
ejpam-6178	279	29	iii	iii	NOUN
ejpam-6178	279	30	)	)	PUNCT
ejpam-6178	279	31	.	.	PUNCT
ejpam-6178	280	1	by	by	ADP
ejpam-6178	280	2	remark	remark	NOUN
ejpam-6178	280	3	2	2	NUM
ejpam-6178	280	4	,	,	PUNCT
ejpam-6178	280	5	f−1(u	f−1(u	PROPN
ejpam-6178	280	6	)	)	PUNCT
ejpam-6178	280	7	is	be	AUX
ejpam-6178	280	8	open	open	ADJ
ejpam-6178	280	9	in	in	ADP
ejpam-6178	280	10	x	x	X
ejpam-6178	280	11	/	/	SYM
ejpam-6178	280	12	s.	s.	PROPN
ejpam-6178	280	13	hence	hence	ADV
ejpam-6178	280	14	,	,	PUNCT
ejpam-6178	280	15	for	for	ADP
ejpam-6178	280	16	any	any	DET
ejpam-6178	280	17	[	[	X
ejpam-6178	280	18	x]s	x]s	PROPN
ejpam-6178	280	19	∈	∈	PROPN
ejpam-6178	280	20	f−1(u	f−1(u	PROPN
ejpam-6178	280	21	)	)	PUNCT
ejpam-6178	280	22	,	,	PUNCT
ejpam-6178	280	23	there	there	PRON
ejpam-6178	280	24	exists	exist	VERB
ejpam-6178	280	25	a	a	DET
ejpam-6178	280	26	neighborhood	neighborhood	NOUN
ejpam-6178	280	27	f−1(w	f−1(w	NOUN
ejpam-6178	280	28	)	)	PUNCT
ejpam-6178	280	29	of	of	ADP
ejpam-6178	280	30	[	[	X
ejpam-6178	280	31	x]s	x]s	NOUN
ejpam-6178	280	32	with	with	ADP
ejpam-6178	280	33	[	[	X
ejpam-6178	280	34	x]s	x]s	PROPN
ejpam-6178	280	35	∈	∈	PROPN
ejpam-6178	280	36	f−1(w	f−1(w	PROPN
ejpam-6178	280	37	)	)	PUNCT
ejpam-6178	280	38	⊆	⊆	NUM
ejpam-6178	280	39	f−1(u	f−1(u	NOUN
ejpam-6178	280	40	)	)	PUNCT
ejpam-6178	280	41	.	.	PUNCT
ejpam-6178	281	1	therefore	therefore	ADV
ejpam-6178	281	2	,	,	PUNCT
ejpam-6178	281	3	f	f	PROPN
ejpam-6178	281	4	is	be	AUX
ejpam-6178	281	5	continuous	continuous	ADJ
ejpam-6178	281	6	.	.	PUNCT
ejpam-6178	282	1	by	by	ADP
ejpam-6178	282	2	claim	claim	NOUN
ejpam-6178	282	3	1,2,3	1,2,3	NUM
ejpam-6178	282	4	,	,	PUNCT
ejpam-6178	282	5	f	f	PROPN
ejpam-6178	282	6	is	be	AUX
ejpam-6178	282	7	a	a	DET
ejpam-6178	282	8	tdb	tdb	PROPN
ejpam-6178	282	9	-	-	NOUN
ejpam-6178	282	10	homomorphism	homomorphism	NOUN
ejpam-6178	282	11	.	.	PUNCT
ejpam-6178	283	1	the	the	DET
ejpam-6178	283	2	next	next	ADJ
ejpam-6178	283	3	corollary	corollary	NOUN
ejpam-6178	283	4	is	be	AUX
ejpam-6178	283	5	a	a	DET
ejpam-6178	283	6	consequence	consequence	NOUN
ejpam-6178	283	7	of	of	ADP
ejpam-6178	283	8	theorem	theorem	ADJ
ejpam-6178	283	9	13	13	NUM
ejpam-6178	283	10	and	and	CCONJ
ejpam-6178	283	11	theorem	theorem	VERB
ejpam-6178	283	12	15	15	NUM
ejpam-6178	283	13	.	.	PUNCT
ejpam-6178	284	1	in	in	ADP
ejpam-6178	284	2	theorem	theorem	NOUN
ejpam-6178	284	3	13	13	NUM
ejpam-6178	284	4	,	,	PUNCT
ejpam-6178	284	5	if	if	SCONJ
ejpam-6178	284	6	a	a	DET
ejpam-6178	284	7	normal	normal	ADJ
ejpam-6178	284	8	db	db	NOUN
ejpam-6178	284	9	-	-	PUNCT
ejpam-6178	284	10	subalgebra	subalgebra	NOUN
ejpam-6178	284	11	s	s	NOUN
ejpam-6178	284	12	is	be	AUX
ejpam-6178	284	13	open	open	ADJ
ejpam-6178	284	14	,	,	PUNCT
ejpam-6178	284	15	the	the	DET
ejpam-6178	284	16	natural	natural	ADJ
ejpam-6178	284	17	db	db	NOUN
ejpam-6178	284	18	-	-	PUNCT
ejpam-6178	284	19	homomorphism	homomorphism	NOUN
ejpam-6178	284	20	with	with	ADP
ejpam-6178	284	21	respect	respect	NOUN
ejpam-6178	284	22	to	to	ADP
ejpam-6178	284	23	s	s	PRON
ejpam-6178	284	24	is	be	AUX
ejpam-6178	284	25	an	an	DET
ejpam-6178	284	26	open	open	ADJ
ejpam-6178	284	27	mapping	mapping	NOUN
ejpam-6178	284	28	which	which	PRON
ejpam-6178	284	29	satisfies	satisfy	VERB
ejpam-6178	284	30	the	the	DET
ejpam-6178	284	31	hypothesis	hypothesis	NOUN
ejpam-6178	284	32	of	of	ADP
ejpam-6178	284	33	theorem	theorem	NOUN
ejpam-6178	284	34	15	15	NUM
ejpam-6178	284	35	.	.	PUNCT
ejpam-6178	284	36	corollary	corollary	ADJ
ejpam-6178	284	37	2	2	NUM
ejpam-6178	284	38	.	.	PUNCT
ejpam-6178	285	1	let	let	VERB
ejpam-6178	285	2	s	s	PRON
ejpam-6178	285	3	and	and	CCONJ
ejpam-6178	285	4	j	j	PROPN
ejpam-6178	285	5	be	be	AUX
ejpam-6178	285	6	normal	normal	ADJ
ejpam-6178	285	7	db	db	NOUN
ejpam-6178	285	8	-	-	PUNCT
ejpam-6178	285	9	subalgebras	subalgebras	PROPN
ejpam-6178	285	10	of	of	ADP
ejpam-6178	285	11	a	a	DET
ejpam-6178	285	12	tdb	tdb	NOUN
ejpam-6178	285	13	-	-	NOUN
ejpam-6178	285	14	algebra	algebra	NOUN
ejpam-6178	285	15	(	(	PUNCT
ejpam-6178	285	16	x	x	X
ejpam-6178	285	17	,	,	PUNCT
ejpam-6178	285	18	◦	◦	NOUN
ejpam-6178	285	19	,	,	PUNCT
ejpam-6178	285	20	τ	τ	X
ejpam-6178	285	21	)	)	PUNCT
ejpam-6178	285	22	such	such	ADJ
ejpam-6178	285	23	that	that	PRON
ejpam-6178	285	24	s	s	PROPN
ejpam-6178	286	1	⊂	⊂	PROPN
ejpam-6178	286	2	j	j	PROPN
ejpam-6178	286	3	.	.	PUNCT
ejpam-6178	287	1	define	define	VERB
ejpam-6178	287	2	a	a	DET
ejpam-6178	287	3	map	map	NOUN
ejpam-6178	287	4	f	f	NOUN
ejpam-6178	287	5	from	from	ADP
ejpam-6178	287	6	(	(	PUNCT
ejpam-6178	287	7	x	x	X
ejpam-6178	287	8	/	/	SYM
ejpam-6178	287	9	s	s	PROPN
ejpam-6178	287	10	,	,	PUNCT
ejpam-6178	287	11	∗	∗	NOUN
ejpam-6178	287	12	,	,	PUNCT
ejpam-6178	287	13	τs	τs	NOUN
ejpam-6178	287	14	)	)	PUNCT
ejpam-6178	287	15	to	to	ADP
ejpam-6178	287	16	(	(	PUNCT
ejpam-6178	287	17	x	x	SYM
ejpam-6178	287	18	/	/	SYM
ejpam-6178	287	19	j	j	PROPN
ejpam-6178	287	20	,	,	PUNCT
ejpam-6178	287	21	∗′	∗′	PROPN
ejpam-6178	287	22	,	,	PUNCT
ejpam-6178	287	23	τj	τj	NOUN
ejpam-6178	287	24	)	)	PUNCT
ejpam-6178	287	25	by	by	ADP
ejpam-6178	287	26	f([x]s	f([x]s	ADJ
ejpam-6178	287	27	)	)	PUNCT
ejpam-6178	287	28	=	=	PUNCT
ejpam-6178	288	1	[	[	X
ejpam-6178	288	2	x]j	x]j	X
ejpam-6178	288	3	for	for	ADP
ejpam-6178	288	4	all	all	PRON
ejpam-6178	288	5	[	[	X
ejpam-6178	288	6	x]s	x]s	PROPN
ejpam-6178	288	7	∈	∈	PROPN
ejpam-6178	288	8	x	x	X
ejpam-6178	288	9	/	/	SYM
ejpam-6178	288	10	s.	s.	PROPN
ejpam-6178	288	11	if	if	SCONJ
ejpam-6178	288	12	s	s	VERB
ejpam-6178	288	13	is	be	AUX
ejpam-6178	288	14	open	open	ADJ
ejpam-6178	288	15	and	and	CCONJ
ejpam-6178	288	16	the	the	DET
ejpam-6178	288	17	natural	natural	ADJ
ejpam-6178	288	18	db	db	NOUN
ejpam-6178	288	19	-	-	PUNCT
ejpam-6178	288	20	homomorphism	homomorphism	NOUN
ejpam-6178	288	21	ψ	ψ	X
ejpam-6178	288	22	from	from	ADP
ejpam-6178	288	23	x	x	PUNCT
ejpam-6178	288	24	onto	onto	ADP
ejpam-6178	288	25	x	x	SYM
ejpam-6178	288	26	/	/	SYM
ejpam-6178	288	27	j	j	PROPN
ejpam-6178	288	28	is	be	AUX
ejpam-6178	288	29	an	an	DET
ejpam-6178	288	30	open	open	ADJ
ejpam-6178	288	31	mapping	mapping	NOUN
ejpam-6178	288	32	,	,	PUNCT
ejpam-6178	288	33	then	then	ADV
ejpam-6178	288	34	f	f	PROPN
ejpam-6178	288	35	is	be	AUX
ejpam-6178	288	36	a	a	DET
ejpam-6178	288	37	tdb	tdb	PROPN
ejpam-6178	288	38	-	-	NOUN
ejpam-6178	288	39	homomorphism	homomorphism	NOUN
ejpam-6178	288	40	.	.	PUNCT
ejpam-6178	289	1	the	the	DET
ejpam-6178	289	2	next	next	ADJ
ejpam-6178	289	3	result	result	NOUN
ejpam-6178	289	4	is	be	AUX
ejpam-6178	289	5	a	a	DET
ejpam-6178	289	6	consequence	consequence	NOUN
ejpam-6178	289	7	of	of	ADP
ejpam-6178	289	8	theorem	theorem	ADJ
ejpam-6178	289	9	13	13	NUM
ejpam-6178	289	10	and	and	CCONJ
ejpam-6178	289	11	corollary	corollary	ADJ
ejpam-6178	289	12	2	2	NUM
ejpam-6178	289	13	.	.	PUNCT
ejpam-6178	289	14	similarly	similarly	ADV
ejpam-6178	289	15	,	,	PUNCT
ejpam-6178	289	16	if	if	SCONJ
ejpam-6178	289	17	a	a	DET
ejpam-6178	289	18	normal	normal	ADJ
ejpam-6178	289	19	db	db	ADJ
ejpam-6178	289	20	-	-	PUNCT
ejpam-6178	289	21	subalgebra	subalgebra	PROPN
ejpam-6178	289	22	j	j	PROPN
ejpam-6178	289	23	is	be	AUX
ejpam-6178	289	24	open	open	ADJ
ejpam-6178	289	25	,	,	PUNCT
ejpam-6178	289	26	the	the	DET
ejpam-6178	289	27	natural	natural	ADJ
ejpam-6178	289	28	db	db	NOUN
ejpam-6178	289	29	-	-	PUNCT
ejpam-6178	289	30	homomorphism	homomorphism	NOUN
ejpam-6178	289	31	with	with	ADP
ejpam-6178	289	32	respect	respect	NOUN
ejpam-6178	289	33	to	to	ADP
ejpam-6178	289	34	j	j	PROPN
ejpam-6178	289	35	is	be	AUX
ejpam-6178	289	36	an	an	DET
ejpam-6178	289	37	open	open	ADJ
ejpam-6178	289	38	mapping	mapping	NOUN
ejpam-6178	289	39	by	by	ADP
ejpam-6178	289	40	theorem	theorem	NOUN
ejpam-6178	289	41	13	13	NUM
ejpam-6178	289	42	which	which	PRON
ejpam-6178	289	43	satisfies	satisfy	VERB
ejpam-6178	289	44	the	the	DET
ejpam-6178	289	45	hypothesis	hypothesis	NOUN
ejpam-6178	289	46	of	of	ADP
ejpam-6178	289	47	corollary	corollary	ADJ
ejpam-6178	289	48	2	2	NUM
ejpam-6178	289	49	.	.	PUNCT
ejpam-6178	289	50	corollary	corollary	ADJ
ejpam-6178	289	51	3	3	NUM
ejpam-6178	289	52	.	.	PUNCT
ejpam-6178	290	1	let	let	VERB
ejpam-6178	290	2	s	s	PRON
ejpam-6178	290	3	and	and	CCONJ
ejpam-6178	290	4	j	j	PROPN
ejpam-6178	290	5	be	be	AUX
ejpam-6178	290	6	normal	normal	ADJ
ejpam-6178	290	7	db	db	NOUN
ejpam-6178	290	8	-	-	PUNCT
ejpam-6178	290	9	subalgebras	subalgebras	PROPN
ejpam-6178	290	10	of	of	ADP
ejpam-6178	290	11	a	a	DET
ejpam-6178	290	12	tdb	tdb	NOUN
ejpam-6178	290	13	-	-	NOUN
ejpam-6178	290	14	algebra	algebra	NOUN
ejpam-6178	290	15	(	(	PUNCT
ejpam-6178	290	16	x	x	X
ejpam-6178	290	17	,	,	PUNCT
ejpam-6178	290	18	◦	◦	NOUN
ejpam-6178	290	19	,	,	PUNCT
ejpam-6178	290	20	τ	τ	X
ejpam-6178	290	21	)	)	PUNCT
ejpam-6178	290	22	such	such	ADJ
ejpam-6178	290	23	that	that	PRON
ejpam-6178	290	24	s	s	PROPN
ejpam-6178	291	1	⊂	⊂	PROPN
ejpam-6178	291	2	j	j	PROPN
ejpam-6178	291	3	.	.	PUNCT
ejpam-6178	292	1	define	define	VERB
ejpam-6178	292	2	a	a	DET
ejpam-6178	292	3	map	map	NOUN
ejpam-6178	292	4	f	f	NOUN
ejpam-6178	292	5	from	from	ADP
ejpam-6178	292	6	(	(	PUNCT
ejpam-6178	292	7	x	x	X
ejpam-6178	292	8	/	/	SYM
ejpam-6178	292	9	s	s	PROPN
ejpam-6178	292	10	,	,	PUNCT
ejpam-6178	292	11	∗	∗	NOUN
ejpam-6178	292	12	,	,	PUNCT
ejpam-6178	292	13	τs	τs	NOUN
ejpam-6178	292	14	)	)	PUNCT
ejpam-6178	292	15	to	to	ADP
ejpam-6178	292	16	(	(	PUNCT
ejpam-6178	292	17	x	x	SYM
ejpam-6178	292	18	/	/	SYM
ejpam-6178	292	19	j	j	PROPN
ejpam-6178	292	20	,	,	PUNCT
ejpam-6178	292	21	∗′	∗′	PROPN
ejpam-6178	292	22	,	,	PUNCT
ejpam-6178	292	23	τj	τj	NOUN
ejpam-6178	292	24	)	)	PUNCT
ejpam-6178	292	25	by	by	ADP
ejpam-6178	292	26	f([x]s	f([x]s	ADJ
ejpam-6178	292	27	)	)	PUNCT
ejpam-6178	292	28	=	=	PUNCT
ejpam-6178	293	1	[	[	X
ejpam-6178	293	2	x]j	x]j	X
ejpam-6178	293	3	for	for	ADP
ejpam-6178	293	4	all	all	PRON
ejpam-6178	293	5	[	[	X
ejpam-6178	293	6	x]s	x]s	PROPN
ejpam-6178	293	7	∈	∈	PROPN
ejpam-6178	293	8	x	x	X
ejpam-6178	293	9	/	/	SYM
ejpam-6178	293	10	s.	s.	PROPN
ejpam-6178	293	11	if	if	SCONJ
ejpam-6178	293	12	s	s	PROPN
ejpam-6178	293	13	and	and	CCONJ
ejpam-6178	293	14	j	j	PROPN
ejpam-6178	293	15	are	be	AUX
ejpam-6178	293	16	open	open	ADJ
ejpam-6178	293	17	,	,	PUNCT
ejpam-6178	293	18	then	then	ADV
ejpam-6178	293	19	f	f	PROPN
ejpam-6178	293	20	is	be	AUX
ejpam-6178	293	21	a	a	DET
ejpam-6178	293	22	tdb	tdb	PROPN
ejpam-6178	293	23	-	-	NOUN
ejpam-6178	293	24	homomorphism	homomorphism	NOUN
ejpam-6178	293	25	.	.	PUNCT
ejpam-6178	294	1	r.	r.	PROPN
ejpam-6178	294	2	nuñez	nuñez	PROPN
ejpam-6178	294	3	,	,	PUNCT
ejpam-6178	294	4	k.	k.	PROPN
ejpam-6178	294	5	b.	b.	PROPN
ejpam-6178	294	6	fuentes	fuentes	PROPN
ejpam-6178	294	7	/	/	SYM
ejpam-6178	294	8	eur	eur	PROPN
ejpam-6178	294	9	.	.	PUNCT
ejpam-6178	295	1	j.	j.	PROPN
ejpam-6178	295	2	pure	pure	PROPN
ejpam-6178	295	3	appl	appl	PROPN
ejpam-6178	295	4	.	.	PROPN
ejpam-6178	295	5	math	math	PROPN
ejpam-6178	295	6	,	,	PUNCT
ejpam-6178	295	7	18	18	NUM
ejpam-6178	295	8	(	(	PUNCT
ejpam-6178	295	9	4	4	NUM
ejpam-6178	295	10	)	)	PUNCT
ejpam-6178	295	11	(	(	PUNCT
ejpam-6178	295	12	2025	2025	NUM
ejpam-6178	295	13	)	)	PUNCT
ejpam-6178	295	14	,	,	PUNCT
ejpam-6178	295	15	6178	6178	NUM
ejpam-6178	295	16	9	9	NUM
ejpam-6178	295	17	of	of	ADP
ejpam-6178	295	18	15	15	NUM
ejpam-6178	295	19	for	for	ADP
ejpam-6178	295	20	a	a	DET
ejpam-6178	295	21	fixed	fix	VERB
ejpam-6178	295	22	element	element	NOUN
ejpam-6178	295	23	s	s	PROPN
ejpam-6178	295	24	of	of	ADP
ejpam-6178	295	25	a	a	DET
ejpam-6178	295	26	tdb	tdb	NOUN
ejpam-6178	295	27	-	-	NOUN
ejpam-6178	295	28	algebra	algebra	NOUN
ejpam-6178	295	29	(	(	PUNCT
ejpam-6178	295	30	x	x	X
ejpam-6178	295	31	,	,	PUNCT
ejpam-6178	295	32	◦	◦	NOUN
ejpam-6178	295	33	,	,	PUNCT
ejpam-6178	295	34	τ	τ	PROPN
ejpam-6178	295	35	)	)	PUNCT
ejpam-6178	295	36	,	,	PUNCT
ejpam-6178	295	37	define	define	VERB
ejpam-6178	295	38	a	a	DET
ejpam-6178	295	39	self	self	NOUN
ejpam-6178	295	40	-	-	PUNCT
ejpam-6178	295	41	map	map	NOUN
ejpam-6178	295	42	fs	fs	ADP
ejpam-6178	295	43	:	:	PUNCT
ejpam-6178	295	44	x	x	SYM
ejpam-6178	295	45	→	→	SYM
ejpam-6178	295	46	x	x	PUNCT
ejpam-6178	295	47	by	by	ADP
ejpam-6178	295	48	fs(x	fs(x	NOUN
ejpam-6178	295	49	)	)	PUNCT
ejpam-6178	295	50	=	=	SYM
ejpam-6178	296	1	x	x	PUNCT
ejpam-6178	296	2	◦	◦	NOUN
ejpam-6178	296	3	s	s	NUM
ejpam-6178	296	4	for	for	ADP
ejpam-6178	296	5	all	all	DET
ejpam-6178	296	6	x	x	SYM
ejpam-6178	296	7	∈	∈	NOUN
ejpam-6178	296	8	x.	x.	NOUN
ejpam-6178	296	9	definition	definition	NOUN
ejpam-6178	296	10	14	14	NUM
ejpam-6178	296	11	.	.	PUNCT
ejpam-6178	297	1	a	a	DET
ejpam-6178	297	2	tdb	tdb	PROPN
ejpam-6178	297	3	-	-	NOUN
ejpam-6178	297	4	algebra	algebra	NOUN
ejpam-6178	297	5	is	be	AUX
ejpam-6178	297	6	said	say	VERB
ejpam-6178	297	7	to	to	PART
ejpam-6178	297	8	be	be	AUX
ejpam-6178	297	9	transitive	transitive	ADJ
ejpam-6178	297	10	open	open	ADJ
ejpam-6178	297	11	if	if	SCONJ
ejpam-6178	297	12	for	for	ADP
ejpam-6178	297	13	each	each	DET
ejpam-6178	297	14	s	s	X
ejpam-6178	297	15	∈	∈	PROPN
ejpam-6178	297	16	x	x	SYM
ejpam-6178	297	17	,	,	PUNCT
ejpam-6178	297	18	the	the	DET
ejpam-6178	297	19	self	self	NOUN
ejpam-6178	297	20	-	-	PUNCT
ejpam-6178	297	21	map	map	NOUN
ejpam-6178	297	22	fs	fs	NOUN
ejpam-6178	297	23	is	be	AUX
ejpam-6178	297	24	open	open	ADJ
ejpam-6178	297	25	and	and	CCONJ
ejpam-6178	297	26	continuous	continuous	ADJ
ejpam-6178	297	27	.	.	PUNCT
ejpam-6178	298	1	the	the	DET
ejpam-6178	298	2	next	next	ADJ
ejpam-6178	298	3	lemma	lemma	PROPN
ejpam-6178	298	4	will	will	AUX
ejpam-6178	298	5	be	be	AUX
ejpam-6178	298	6	used	use	VERB
ejpam-6178	298	7	to	to	PART
ejpam-6178	298	8	prove	prove	VERB
ejpam-6178	298	9	additional	additional	ADJ
ejpam-6178	298	10	tdb	tdb	NOUN
ejpam-6178	298	11	-	-	NOUN
ejpam-6178	298	12	homomorphism	homomorphism	NOUN
ejpam-6178	298	13	between	between	ADP
ejpam-6178	298	14	transitive	transitive	ADJ
ejpam-6178	298	15	open	open	ADJ
ejpam-6178	298	16	tdb	tdb	NOUN
ejpam-6178	298	17	-	-	PUNCT
ejpam-6178	298	18	algebras	algebras	PROPN
ejpam-6178	298	19	.	.	PUNCT
ejpam-6178	299	1	lemma	lemma	PROPN
ejpam-6178	299	2	2	2	X
ejpam-6178	299	3	.	.	PUNCT
ejpam-6178	299	4	let	let	VERB
ejpam-6178	299	5	a	a	PRON
ejpam-6178	299	6	be	be	AUX
ejpam-6178	299	7	open	open	ADJ
ejpam-6178	299	8	in	in	ADP
ejpam-6178	299	9	a	a	DET
ejpam-6178	299	10	transitive	transitive	ADJ
ejpam-6178	299	11	open	open	ADJ
ejpam-6178	299	12	tdb	tdb	NOUN
ejpam-6178	299	13	-	-	NOUN
ejpam-6178	299	14	algebra	algebra	NOUN
ejpam-6178	299	15	(	(	PUNCT
ejpam-6178	299	16	x	x	X
ejpam-6178	299	17	,	,	PUNCT
ejpam-6178	299	18	◦	◦	NOUN
ejpam-6178	299	19	,	,	PUNCT
ejpam-6178	299	20	τ	τ	X
ejpam-6178	299	21	)	)	PUNCT
ejpam-6178	299	22	and	and	CCONJ
ejpam-6178	299	23	x	x	PUNCT
ejpam-6178	299	24	∈	∈	PROPN
ejpam-6178	299	25	x.	x.	NOUN
ejpam-6178	299	26	then	then	ADV
ejpam-6178	299	27	the	the	DET
ejpam-6178	299	28	following	follow	VERB
ejpam-6178	299	29	statements	statement	NOUN
ejpam-6178	299	30	hold	hold	VERB
ejpam-6178	299	31	:	:	PUNCT
ejpam-6178	299	32	(	(	PUNCT
ejpam-6178	299	33	i	i	NOUN
ejpam-6178	299	34	)	)	PUNCT
ejpam-6178	299	35	fx(a	fx(a	NOUN
ejpam-6178	299	36	)	)	PUNCT
ejpam-6178	299	37	=	=	SYM
ejpam-6178	299	38	a	a	DET
ejpam-6178	299	39	◦	◦	NOUN
ejpam-6178	299	40	x	x	PUNCT
ejpam-6178	299	41	is	be	AUX
ejpam-6178	299	42	open	open	ADJ
ejpam-6178	299	43	in	in	ADP
ejpam-6178	299	44	x	x	NOUN
ejpam-6178	299	45	;	;	PUNCT
ejpam-6178	299	46	and	and	CCONJ
ejpam-6178	299	47	(	(	PUNCT
ejpam-6178	299	48	ii	ii	NOUN
ejpam-6178	299	49	)	)	PUNCT
ejpam-6178	299	50	f−1	f−1	PROPN
ejpam-6178	299	51	x	x	SYM
ejpam-6178	299	52	(	(	PUNCT
ejpam-6178	299	53	a	a	X
ejpam-6178	299	54	)	)	PUNCT
ejpam-6178	300	1	=	=	SYM
ejpam-6178	300	2	{	{	PUNCT
ejpam-6178	300	3	y	y	PROPN
ejpam-6178	300	4	∈	∈	PROPN
ejpam-6178	300	5	x	x	X
ejpam-6178	300	6	|	|	ADV
ejpam-6178	300	7	y	y	PROPN
ejpam-6178	300	8	◦	◦	NOUN
ejpam-6178	300	9	x	x	X
ejpam-6178	300	10	=	=	SYM
ejpam-6178	300	11	fx(y	fx(y	X
ejpam-6178	300	12	)	)	PUNCT
ejpam-6178	300	13	∈	∈	PROPN
ejpam-6178	300	14	a	a	PRON
ejpam-6178	300	15	}	}	PUNCT
ejpam-6178	300	16	is	be	AUX
ejpam-6178	300	17	open	open	ADJ
ejpam-6178	300	18	in	in	ADP
ejpam-6178	300	19	x.	x.	NOUN
ejpam-6178	300	20	proof	proof	NOUN
ejpam-6178	300	21	.	.	PUNCT
ejpam-6178	301	1	since	since	SCONJ
ejpam-6178	301	2	x	x	PRON
ejpam-6178	301	3	is	be	AUX
ejpam-6178	301	4	a	a	DET
ejpam-6178	301	5	transitive	transitive	ADJ
ejpam-6178	301	6	open	open	ADJ
ejpam-6178	301	7	tdb	tdb	NOUN
ejpam-6178	301	8	-	-	NOUN
ejpam-6178	301	9	algebra	algebra	NOUN
ejpam-6178	301	10	,	,	PUNCT
ejpam-6178	301	11	it	it	PRON
ejpam-6178	301	12	follows	follow	VERB
ejpam-6178	301	13	that	that	SCONJ
ejpam-6178	301	14	fx	fx	PROPN
ejpam-6178	301	15	is	be	AUX
ejpam-6178	301	16	open	open	ADJ
ejpam-6178	301	17	and	and	CCONJ
ejpam-6178	301	18	continuous	continuous	ADJ
ejpam-6178	301	19	.	.	PUNCT
ejpam-6178	302	1	since	since	SCONJ
ejpam-6178	302	2	a	a	PRON
ejpam-6178	302	3	is	be	AUX
ejpam-6178	302	4	open	open	ADJ
ejpam-6178	302	5	in	in	ADP
ejpam-6178	302	6	x	x	NOUN
ejpam-6178	302	7	,	,	PUNCT
ejpam-6178	302	8	fx(a	fx(a	NOUN
ejpam-6178	302	9	)	)	PUNCT
ejpam-6178	302	10	=	=	PRON
ejpam-6178	303	1	{	{	PUNCT
ejpam-6178	303	2	y	y	PROPN
ejpam-6178	303	3	∈	∈	PROPN
ejpam-6178	303	4	x	x	INTJ
ejpam-6178	304	1	|	|	ADV
ejpam-6178	304	2	y	y	NOUN
ejpam-6178	304	3	=	=	PUNCT
ejpam-6178	304	4	fx(a	fx(a	X
ejpam-6178	304	5	)	)	PUNCT
ejpam-6178	304	6	for	for	ADP
ejpam-6178	304	7	some	some	DET
ejpam-6178	304	8	a	a	DET
ejpam-6178	304	9	∈	∈	PROPN
ejpam-6178	304	10	a	a	DET
ejpam-6178	304	11	}	}	PUNCT
ejpam-6178	304	12	=	=	SYM
ejpam-6178	304	13	{	{	PUNCT
ejpam-6178	304	14	y	y	PROPN
ejpam-6178	304	15	∈	∈	PROPN
ejpam-6178	304	16	x	x	X
ejpam-6178	305	1	|	|	ADV
ejpam-6178	305	2	y	y	NOUN
ejpam-6178	305	3	=	=	PUNCT
ejpam-6178	305	4	a	a	DET
ejpam-6178	305	5	◦	◦	NOUN
ejpam-6178	305	6	x	x	PUNCT
ejpam-6178	305	7	for	for	ADP
ejpam-6178	305	8	some	some	DET
ejpam-6178	305	9	a	a	DET
ejpam-6178	305	10	∈	∈	PROPN
ejpam-6178	305	11	a	a	DET
ejpam-6178	305	12	}	}	PUNCT
ejpam-6178	305	13	=	=	SYM
ejpam-6178	305	14	{	{	PUNCT
ejpam-6178	305	15	a	a	DET
ejpam-6178	305	16	◦	◦	NOUN
ejpam-6178	305	17	x	x	SYM
ejpam-6178	305	18	|	|	ADV
ejpam-6178	305	19	a	a	DET
ejpam-6178	305	20	∈	∈	NOUN
ejpam-6178	305	21	a	a	PRON
ejpam-6178	305	22	}	}	PUNCT
ejpam-6178	305	23	=	=	SYM
ejpam-6178	305	24	a	a	DET
ejpam-6178	305	25	◦	◦	NOUN
ejpam-6178	305	26	x	x	PUNCT
ejpam-6178	305	27	is	be	AUX
ejpam-6178	305	28	open	open	ADJ
ejpam-6178	305	29	in	in	ADP
ejpam-6178	305	30	x.	x.	NOUN
ejpam-6178	305	31	and	and	CCONJ
ejpam-6178	305	32	f−1	f−1	PROPN
ejpam-6178	305	33	x	x	SYM
ejpam-6178	305	34	(	(	PUNCT
ejpam-6178	305	35	a	a	X
ejpam-6178	305	36	)	)	PUNCT
ejpam-6178	305	37	=	=	SYM
ejpam-6178	306	1	{	{	PUNCT
ejpam-6178	306	2	y	y	PROPN
ejpam-6178	306	3	∈	∈	PROPN
ejpam-6178	306	4	x	x	X
ejpam-6178	306	5	|	|	ADV
ejpam-6178	306	6	y	y	PROPN
ejpam-6178	306	7	◦	◦	NOUN
ejpam-6178	306	8	x	x	X
ejpam-6178	306	9	=	=	SYM
ejpam-6178	306	10	fx(y	fx(y	X
ejpam-6178	306	11	)	)	PUNCT
ejpam-6178	306	12	∈	∈	PROPN
ejpam-6178	306	13	a	a	PRON
ejpam-6178	306	14	}	}	PUNCT
ejpam-6178	306	15	is	be	AUX
ejpam-6178	306	16	open	open	ADJ
ejpam-6178	306	17	in	in	ADP
ejpam-6178	306	18	x.	x.	NOUN
ejpam-6178	306	19	the	the	DET
ejpam-6178	306	20	next	next	ADJ
ejpam-6178	306	21	theorem	theorem	NOUN
ejpam-6178	306	22	obtains	obtain	VERB
ejpam-6178	306	23	a	a	DET
ejpam-6178	306	24	tdb	tdb	PROPN
ejpam-6178	306	25	-	-	NOUN
ejpam-6178	306	26	homomorphism	homomorphism	NOUN
ejpam-6178	306	27	and	and	CCONJ
ejpam-6178	306	28	tdb	tdb	PROPN
ejpam-6178	306	29	-	-	NOUN
ejpam-6178	306	30	isomorphism	isomorphism	NOUN
ejpam-6178	306	31	between	between	ADP
ejpam-6178	306	32	two	two	NUM
ejpam-6178	306	33	transitive	transitive	ADJ
ejpam-6178	306	34	open	open	ADJ
ejpam-6178	306	35	tdb	tdb	NOUN
ejpam-6178	306	36	-	-	PUNCT
ejpam-6178	306	37	algebras	algebras	PROPN
ejpam-6178	306	38	with	with	ADP
ejpam-6178	306	39	some	some	DET
ejpam-6178	306	40	conditions	condition	NOUN
ejpam-6178	306	41	to	to	PART
ejpam-6178	306	42	hold	hold	VERB
ejpam-6178	306	43	.	.	PUNCT
ejpam-6178	307	1	theorem	theorem	NOUN
ejpam-6178	307	2	16	16	NUM
ejpam-6178	307	3	.	.	PUNCT
ejpam-6178	308	1	let	let	VERB
ejpam-6178	308	2	x	x	PRON
ejpam-6178	308	3	and	and	CCONJ
ejpam-6178	308	4	y	y	PROPN
ejpam-6178	308	5	be	be	AUX
ejpam-6178	308	6	transitive	transitive	ADJ
ejpam-6178	308	7	open	open	ADJ
ejpam-6178	308	8	tdb	tdb	NOUN
ejpam-6178	308	9	-	-	PUNCT
ejpam-6178	308	10	algebras	algebras	PROPN
ejpam-6178	308	11	and	and	CCONJ
ejpam-6178	308	12	g	g	PROPN
ejpam-6178	308	13	a	a	DET
ejpam-6178	308	14	db	db	NOUN
ejpam-6178	308	15	-	-	PUNCT
ejpam-6178	308	16	homomorphism	homomorphism	NOUN
ejpam-6178	308	17	from	from	ADP
ejpam-6178	308	18	(	(	PUNCT
ejpam-6178	308	19	x	x	NOUN
ejpam-6178	308	20	,	,	PUNCT
ejpam-6178	308	21	◦	◦	NOUN
ejpam-6178	308	22	,	,	PUNCT
ejpam-6178	308	23	1x	1x	NUM
ejpam-6178	308	24	)	)	PUNCT
ejpam-6178	308	25	to	to	ADP
ejpam-6178	308	26	(	(	PUNCT
ejpam-6178	308	27	y	y	PROPN
ejpam-6178	308	28	,	,	PUNCT
ejpam-6178	308	29	∗	∗	NOUN
ejpam-6178	308	30	,	,	PUNCT
ejpam-6178	308	31	1y	1y	NOUN
ejpam-6178	308	32	)	)	PUNCT
ejpam-6178	308	33	.	.	PUNCT
ejpam-6178	309	1	then	then	ADV
ejpam-6178	309	2	the	the	DET
ejpam-6178	309	3	following	following	ADJ
ejpam-6178	309	4	statements	statement	NOUN
ejpam-6178	309	5	hold	hold	VERB
ejpam-6178	309	6	:	:	PUNCT
ejpam-6178	309	7	(	(	PUNCT
ejpam-6178	309	8	i	i	NOUN
ejpam-6178	309	9	)	)	PUNCT
ejpam-6178	309	10	if	if	SCONJ
ejpam-6178	309	11	for	for	ADP
ejpam-6178	309	12	each	each	DET
ejpam-6178	309	13	neighborhood	neighborhood	NOUN
ejpam-6178	309	14	u	u	NOUN
ejpam-6178	309	15	of	of	ADP
ejpam-6178	309	16	1y	1y	PROPN
ejpam-6178	309	17	in	in	ADP
ejpam-6178	309	18	y	y	PROPN
ejpam-6178	309	19	,	,	PUNCT
ejpam-6178	309	20	there	there	PRON
ejpam-6178	309	21	exists	exist	VERB
ejpam-6178	309	22	a	a	DET
ejpam-6178	309	23	neighborhood	neighborhood	NOUN
ejpam-6178	309	24	of	of	ADP
ejpam-6178	309	25	v	v	NOUN
ejpam-6178	309	26	of	of	ADP
ejpam-6178	309	27	1x	1x	NUM
ejpam-6178	309	28	in	in	ADP
ejpam-6178	309	29	x	x	PUNCT
ejpam-6178	309	30	such	such	ADJ
ejpam-6178	309	31	that	that	SCONJ
ejpam-6178	309	32	g(v	g(v	PROPN
ejpam-6178	309	33	)	)	PUNCT
ejpam-6178	309	34	⊆	⊆	NUM
ejpam-6178	309	35	u	u	NOUN
ejpam-6178	309	36	,	,	PUNCT
ejpam-6178	309	37	then	then	ADV
ejpam-6178	309	38	g	g	PROPN
ejpam-6178	309	39	is	be	AUX
ejpam-6178	309	40	a	a	DET
ejpam-6178	309	41	continuous	continuous	ADJ
ejpam-6178	309	42	mapping	mapping	NOUN
ejpam-6178	309	43	.	.	PUNCT
ejpam-6178	310	1	that	that	PRON
ejpam-6178	310	2	is	be	AUX
ejpam-6178	310	3	,	,	PUNCT
ejpam-6178	310	4	g	g	PROPN
ejpam-6178	310	5	is	be	AUX
ejpam-6178	310	6	a	a	DET
ejpam-6178	310	7	tdbhomomorphism	tdbhomomorphism	NOUN
ejpam-6178	310	8	;	;	PUNCT
ejpam-6178	310	9	and	and	CCONJ
ejpam-6178	310	10	(	(	PUNCT
ejpam-6178	310	11	ii	ii	NOUN
ejpam-6178	310	12	)	)	PUNCT
ejpam-6178	310	13	if	if	SCONJ
ejpam-6178	310	14	for	for	ADP
ejpam-6178	310	15	each	each	DET
ejpam-6178	310	16	neighborhood	neighborhood	NOUN
ejpam-6178	310	17	of	of	ADP
ejpam-6178	310	18	v	v	NOUN
ejpam-6178	310	19	of	of	ADP
ejpam-6178	310	20	1x	1x	NUM
ejpam-6178	310	21	in	in	ADP
ejpam-6178	310	22	x	x	NOUN
ejpam-6178	310	23	,	,	PUNCT
ejpam-6178	310	24	there	there	PRON
ejpam-6178	310	25	exists	exist	VERB
ejpam-6178	310	26	a	a	DET
ejpam-6178	310	27	neighborhood	neighborhood	NOUN
ejpam-6178	310	28	u	u	NOUN
ejpam-6178	310	29	of	of	ADP
ejpam-6178	310	30	1y	1y	PROPN
ejpam-6178	310	31	in	in	ADP
ejpam-6178	310	32	y	y	PRON
ejpam-6178	310	33	such	such	ADJ
ejpam-6178	310	34	that	that	SCONJ
ejpam-6178	310	35	y	y	PROPN
ejpam-6178	310	36	⊆	⊆	NUM
ejpam-6178	310	37	g(v	g(v	PROPN
ejpam-6178	310	38	)	)	PUNCT
ejpam-6178	310	39	,	,	PUNCT
ejpam-6178	310	40	then	then	ADV
ejpam-6178	310	41	g	g	PROPN
ejpam-6178	310	42	is	be	AUX
ejpam-6178	310	43	an	an	DET
ejpam-6178	310	44	open	open	ADJ
ejpam-6178	310	45	mapping	mapping	NOUN
ejpam-6178	310	46	.	.	PUNCT
ejpam-6178	311	1	proof	proof	NOUN
ejpam-6178	311	2	.	.	PUNCT
ejpam-6178	312	1	(	(	PUNCT
ejpam-6178	312	2	i	i	NOUN
ejpam-6178	312	3	)	)	PUNCT
ejpam-6178	312	4	assume	assume	VERB
ejpam-6178	312	5	that	that	SCONJ
ejpam-6178	312	6	a	a	PRON
ejpam-6178	312	7	is	be	AUX
ejpam-6178	312	8	open	open	ADJ
ejpam-6178	312	9	in	in	ADP
ejpam-6178	312	10	y	y	PROPN
ejpam-6178	312	11	.	.	PUNCT
ejpam-6178	313	1	if	if	SCONJ
ejpam-6178	313	2	a	a	DET
ejpam-6178	313	3	∩	∩	NOUN
ejpam-6178	313	4	im(g	im(g	PRON
ejpam-6178	313	5	)	)	PUNCT
ejpam-6178	313	6	=	=	SYM
ejpam-6178	313	7	∅	∅	NOUN
ejpam-6178	313	8	,	,	PUNCT
ejpam-6178	313	9	then	then	ADV
ejpam-6178	313	10	g−1(a	g−1(a	PROPN
ejpam-6178	313	11	)	)	PUNCT
ejpam-6178	313	12	=	=	PUNCT
ejpam-6178	313	13	∅	∅	NOUN
ejpam-6178	313	14	,	,	PUNCT
ejpam-6178	313	15	which	which	PRON
ejpam-6178	313	16	is	be	AUX
ejpam-6178	313	17	open	open	ADJ
ejpam-6178	313	18	in	in	ADP
ejpam-6178	313	19	x.	x.	NOUN
ejpam-6178	313	20	suppose	suppose	VERB
ejpam-6178	313	21	a∩	a∩	PROPN
ejpam-6178	313	22	im(g	im(g	PUNCT
ejpam-6178	313	23	)	)	PUNCT
ejpam-6178	313	24	̸=	̸=	NOUN
ejpam-6178	313	25	∅	∅	NOUN
ejpam-6178	313	26	and	and	CCONJ
ejpam-6178	313	27	x	x	PUNCT
ejpam-6178	313	28	∈	∈	PROPN
ejpam-6178	313	29	g−1(a	g−1(a	NOUN
ejpam-6178	313	30	)	)	PUNCT
ejpam-6178	313	31	.	.	PUNCT
ejpam-6178	314	1	then	then	ADV
ejpam-6178	314	2	g(x	g(x	NOUN
ejpam-6178	314	3	)	)	PUNCT
ejpam-6178	315	1	=	=	SYM
ejpam-6178	315	2	∈	∈	PROPN
ejpam-6178	315	3	a∩	a∩	PROPN
ejpam-6178	315	4	im(g	im(g	PUNCT
ejpam-6178	315	5	)	)	PUNCT
ejpam-6178	315	6	.	.	PUNCT
ejpam-6178	316	1	since	since	SCONJ
ejpam-6178	316	2	y	y	PROPN
ejpam-6178	316	3	is	be	AUX
ejpam-6178	316	4	transitive	transitive	ADJ
ejpam-6178	316	5	open	open	ADJ
ejpam-6178	316	6	and	and	CCONJ
ejpam-6178	316	7	by	by	ADP
ejpam-6178	316	8	lemma	lemma	PROPN
ejpam-6178	316	9	2	2	NUM
ejpam-6178	316	10	(	(	PUNCT
ejpam-6178	316	11	ii	ii	NOUN
ejpam-6178	316	12	)	)	PUNCT
ejpam-6178	316	13	,	,	PUNCT
ejpam-6178	316	14	f−1	f−1	PROPN
ejpam-6178	316	15	g(x)(a	g(x)(a	NOUN
ejpam-6178	316	16	)	)	PUNCT
ejpam-6178	316	17	is	be	AUX
ejpam-6178	316	18	open	open	ADJ
ejpam-6178	316	19	in	in	ADP
ejpam-6178	316	20	y	y	PROPN
ejpam-6178	316	21	.	.	PUNCT
ejpam-6178	317	1	let	let	VERB
ejpam-6178	317	2	b	b	NOUN
ejpam-6178	317	3	=	=	SYM
ejpam-6178	317	4	f−1	f−1	PROPN
ejpam-6178	317	5	g(x)(a	g(x)(a	NOUN
ejpam-6178	317	6	)	)	PUNCT
ejpam-6178	317	7	.	.	PUNCT
ejpam-6178	318	1	note	note	VERB
ejpam-6178	318	2	that	that	SCONJ
ejpam-6178	318	3	by	by	ADP
ejpam-6178	318	4	db2	db2	PROPN
ejpam-6178	318	5	,	,	PUNCT
ejpam-6178	318	6	g(x	g(x	NOUN
ejpam-6178	318	7	)	)	PUNCT
ejpam-6178	319	1	=	=	SYM
ejpam-6178	319	2	1y	1y	PROPN
ejpam-6178	319	3	∗	∗	X
ejpam-6178	319	4	g(x	g(x	NOUN
ejpam-6178	319	5	)	)	PUNCT
ejpam-6178	319	6	=	=	SYM
ejpam-6178	319	7	fg(x)(1y	fg(x)(1y	ADJ
ejpam-6178	319	8	)	)	PUNCT
ejpam-6178	319	9	∈	∈	PROPN
ejpam-6178	319	10	a.	a.	NOUN
ejpam-6178	319	11	hence	hence	ADV
ejpam-6178	319	12	,	,	PUNCT
ejpam-6178	319	13	1y	1y	PROPN
ejpam-6178	319	14	∈	∈	PROPN
ejpam-6178	319	15	b.	b.	PROPN
ejpam-6178	319	16	that	that	ADV
ejpam-6178	319	17	is	be	AUX
ejpam-6178	319	18	,	,	PUNCT
ejpam-6178	319	19	b	b	PROPN
ejpam-6178	319	20	is	be	AUX
ejpam-6178	319	21	a	a	DET
ejpam-6178	319	22	neighborhood	neighborhood	NOUN
ejpam-6178	319	23	of	of	ADP
ejpam-6178	319	24	1y	1y	NUM
ejpam-6178	319	25	.	.	PUNCT
ejpam-6178	320	1	by	by	ADP
ejpam-6178	320	2	hypothesis	hypothesis	NOUN
ejpam-6178	320	3	,	,	PUNCT
ejpam-6178	320	4	there	there	PRON
ejpam-6178	320	5	exists	exist	VERB
ejpam-6178	320	6	a	a	DET
ejpam-6178	320	7	neighborhood	neighborhood	NOUN
ejpam-6178	320	8	v	v	NOUN
ejpam-6178	320	9	of	of	ADP
ejpam-6178	320	10	1x	1x	NUM
ejpam-6178	320	11	in	in	ADP
ejpam-6178	320	12	x	x	PUNCT
ejpam-6178	320	13	such	such	ADJ
ejpam-6178	320	14	that	that	SCONJ
ejpam-6178	320	15	g(v	g(v	PROPN
ejpam-6178	320	16	)	)	PUNCT
ejpam-6178	320	17	⊆	⊆	NUM
ejpam-6178	320	18	b.	b.	PROPN
ejpam-6178	320	19	note	note	NOUN
ejpam-6178	321	1	that	that	SCONJ
ejpam-6178	321	2	v	v	X
ejpam-6178	321	3	◦	◦	NOUN
ejpam-6178	321	4	x	x	PUNCT
ejpam-6178	321	5	is	be	AUX
ejpam-6178	321	6	open	open	ADJ
ejpam-6178	321	7	in	in	ADP
ejpam-6178	321	8	x	x	PUNCT
ejpam-6178	321	9	by	by	ADP
ejpam-6178	321	10	lemma	lemma	PROPN
ejpam-6178	321	11	2	2	PROPN
ejpam-6178	321	12	(	(	PUNCT
ejpam-6178	321	13	i	i	NOUN
ejpam-6178	321	14	)	)	PUNCT
ejpam-6178	321	15	.	.	PUNCT
ejpam-6178	322	1	by	by	ADP
ejpam-6178	322	2	db2	db2	PROPN
ejpam-6178	322	3	,	,	PUNCT
ejpam-6178	322	4	x	x	PUNCT
ejpam-6178	322	5	=	=	SYM
ejpam-6178	322	6	1x	1x	NUM
ejpam-6178	322	7	◦	◦	NOUN
ejpam-6178	322	8	x	x	SYM
ejpam-6178	322	9	∈	∈	NOUN
ejpam-6178	322	10	v	v	ADP
ejpam-6178	322	11	◦	◦	NOUN
ejpam-6178	322	12	x.	x.	NOUN
ejpam-6178	322	13	note	note	VERB
ejpam-6178	322	14	that	that	SCONJ
ejpam-6178	322	15	for	for	ADP
ejpam-6178	322	16	any	any	PRON
ejpam-6178	322	17	v	v	NUM
ejpam-6178	322	18	∈	∈	PROPN
ejpam-6178	322	19	b	b	NOUN
ejpam-6178	322	20	,	,	PUNCT
ejpam-6178	322	21	v	v	NOUN
ejpam-6178	322	22	∗	∗	NOUN
ejpam-6178	322	23	g(x	g(x	NOUN
ejpam-6178	322	24	)	)	PUNCT
ejpam-6178	322	25	∈	∈	PROPN
ejpam-6178	322	26	b	b	NOUN
ejpam-6178	322	27	∗	∗	X
ejpam-6178	322	28	g(x	g(x	NOUN
ejpam-6178	322	29	)	)	PUNCT
ejpam-6178	322	30	.	.	PUNCT
ejpam-6178	323	1	also	also	ADV
ejpam-6178	323	2	,	,	PUNCT
ejpam-6178	323	3	v	v	ADP
ejpam-6178	323	4	∗	∗	X
ejpam-6178	323	5	g(x	g(x	NOUN
ejpam-6178	323	6	)	)	PUNCT
ejpam-6178	323	7	=	=	SYM
ejpam-6178	323	8	fg(x)(v	fg(x)(v	X
ejpam-6178	323	9	)	)	PUNCT
ejpam-6178	323	10	∈	∈	PROPN
ejpam-6178	323	11	a.	a.	NOUN
ejpam-6178	323	12	then	then	ADV
ejpam-6178	323	13	b	b	X
ejpam-6178	323	14	∗	∗	X
ejpam-6178	323	15	g(x	g(x	NOUN
ejpam-6178	323	16	)	)	PUNCT
ejpam-6178	324	1	⊆	⊆	NUM
ejpam-6178	324	2	a.	a.	NOUN
ejpam-6178	324	3	now	now	ADV
ejpam-6178	324	4	,	,	PUNCT
ejpam-6178	324	5	g(v	g(v	PROPN
ejpam-6178	324	6	◦	◦	NOUN
ejpam-6178	324	7	x	x	NOUN
ejpam-6178	324	8	)	)	PUNCT
ejpam-6178	324	9	=	=	SYM
ejpam-6178	324	10	g(v	g(v	PROPN
ejpam-6178	324	11	)	)	PUNCT
ejpam-6178	324	12	∗	∗	NOUN
ejpam-6178	324	13	g(x	g(x	NOUN
ejpam-6178	324	14	)	)	PUNCT
ejpam-6178	324	15	⊆	⊆	NUM
ejpam-6178	324	16	b	b	NOUN
ejpam-6178	324	17	∗	∗	X
ejpam-6178	324	18	g(x	g(x	NOUN
ejpam-6178	324	19	)	)	PUNCT
ejpam-6178	324	20	⊆	⊆	NUM
ejpam-6178	324	21	a.	a.	NOUN
ejpam-6178	324	22	thus	thus	ADV
ejpam-6178	324	23	,	,	PUNCT
ejpam-6178	324	24	x	x	PUNCT
ejpam-6178	324	25	∈	∈	NOUN
ejpam-6178	324	26	v	v	ADP
ejpam-6178	324	27	◦	◦	NOUN
ejpam-6178	324	28	x	x	SYM
ejpam-6178	324	29	⊆	⊆	NUM
ejpam-6178	324	30	g−1(g(v	g−1(g(v	ADJ
ejpam-6178	324	31	◦	◦	NOUN
ejpam-6178	324	32	x	x	NOUN
ejpam-6178	324	33	)	)	PUNCT
ejpam-6178	324	34	)	)	PUNCT
ejpam-6178	325	1	⊆	⊆	NUM
ejpam-6178	325	2	g−1(a	g−1(a	NOUN
ejpam-6178	325	3	)	)	PUNCT
ejpam-6178	325	4	.	.	PUNCT
ejpam-6178	326	1	therefore	therefore	ADV
ejpam-6178	326	2	,	,	PUNCT
ejpam-6178	326	3	for	for	ADP
ejpam-6178	326	4	all	all	DET
ejpam-6178	326	5	x	x	SYM
ejpam-6178	326	6	∈	∈	PROPN
ejpam-6178	326	7	g−1(a	g−1(a	NOUN
ejpam-6178	326	8	)	)	PUNCT
ejpam-6178	326	9	there	there	PRON
ejpam-6178	326	10	exist	exist	VERB
ejpam-6178	326	11	a	a	DET
ejpam-6178	326	12	neighborhood	neighborhood	NOUN
ejpam-6178	326	13	v	v	ADP
ejpam-6178	326	14	◦	◦	NOUN
ejpam-6178	326	15	x	x	SYM
ejpam-6178	326	16	of	of	ADP
ejpam-6178	326	17	x	x	PUNCT
ejpam-6178	326	18	in	in	ADP
ejpam-6178	326	19	x	x	X
ejpam-6178	326	20	such	such	ADJ
ejpam-6178	326	21	that	that	SCONJ
ejpam-6178	326	22	r.	r.	PROPN
ejpam-6178	326	23	nuñez	nuñez	PROPN
ejpam-6178	326	24	,	,	PUNCT
ejpam-6178	326	25	k.	k.	PROPN
ejpam-6178	326	26	b.	b.	PROPN
ejpam-6178	326	27	fuentes	fuentes	PROPN
ejpam-6178	326	28	/	/	SYM
ejpam-6178	326	29	eur	eur	PROPN
ejpam-6178	326	30	.	.	PUNCT
ejpam-6178	327	1	j.	j.	PROPN
ejpam-6178	327	2	pure	pure	PROPN
ejpam-6178	327	3	appl	appl	PROPN
ejpam-6178	327	4	.	.	PROPN
ejpam-6178	327	5	math	math	PROPN
ejpam-6178	327	6	,	,	PUNCT
ejpam-6178	327	7	18	18	NUM
ejpam-6178	327	8	(	(	PUNCT
ejpam-6178	327	9	4	4	NUM
ejpam-6178	327	10	)	)	PUNCT
ejpam-6178	327	11	(	(	PUNCT
ejpam-6178	327	12	2025	2025	NUM
ejpam-6178	327	13	)	)	PUNCT
ejpam-6178	327	14	,	,	PUNCT
ejpam-6178	327	15	6178	6178	NUM
ejpam-6178	327	16	10	10	NUM
ejpam-6178	327	17	of	of	ADP
ejpam-6178	327	18	15	15	NUM
ejpam-6178	327	19	v	v	NOUN
ejpam-6178	327	20	◦	◦	NOUN
ejpam-6178	327	21	x	x	SYM
ejpam-6178	327	22	⊆	⊆	NUM
ejpam-6178	327	23	g−1(a	g−1(a	NOUN
ejpam-6178	327	24	)	)	PUNCT
ejpam-6178	327	25	.	.	PUNCT
ejpam-6178	328	1	by	by	ADP
ejpam-6178	328	2	remark	remark	NOUN
ejpam-6178	328	3	2	2	NUM
ejpam-6178	328	4	,	,	PUNCT
ejpam-6178	328	5	g−1(a	g−1(a	PROPN
ejpam-6178	328	6	)	)	PUNCT
ejpam-6178	328	7	is	be	AUX
ejpam-6178	328	8	open	open	ADJ
ejpam-6178	328	9	in	in	ADP
ejpam-6178	328	10	x.	x.	NOUN
ejpam-6178	328	11	therefore	therefore	ADV
ejpam-6178	328	12	,	,	PUNCT
ejpam-6178	328	13	g	g	PROPN
ejpam-6178	328	14	is	be	AUX
ejpam-6178	328	15	continuous	continuous	ADJ
ejpam-6178	328	16	.	.	PUNCT
ejpam-6178	329	1	(	(	PUNCT
ejpam-6178	329	2	ii	ii	NOUN
ejpam-6178	329	3	)	)	PUNCT
ejpam-6178	329	4	assume	assume	VERB
ejpam-6178	329	5	that	that	SCONJ
ejpam-6178	329	6	a	a	PRON
ejpam-6178	329	7	is	be	AUX
ejpam-6178	329	8	open	open	ADJ
ejpam-6178	329	9	in	in	ADP
ejpam-6178	329	10	x.	x.	NOUN
ejpam-6178	329	11	let	let	VERB
ejpam-6178	329	12	y	y	PROPN
ejpam-6178	329	13	∈	∈	PROPN
ejpam-6178	329	14	g(a	g(a	PROPN
ejpam-6178	329	15	)	)	PUNCT
ejpam-6178	329	16	.	.	PUNCT
ejpam-6178	330	1	then	then	ADV
ejpam-6178	330	2	y	y	PROPN
ejpam-6178	330	3	=	=	PUNCT
ejpam-6178	330	4	g(x	g(x	PROPN
ejpam-6178	330	5	)	)	PUNCT
ejpam-6178	330	6	for	for	ADP
ejpam-6178	330	7	some	some	DET
ejpam-6178	330	8	x	x	SYM
ejpam-6178	330	9	∈	∈	PROPN
ejpam-6178	330	10	a.	a.	NOUN
ejpam-6178	330	11	note	note	NOUN
ejpam-6178	330	12	that	that	SCONJ
ejpam-6178	330	13	f−1	f−1	PROPN
ejpam-6178	330	14	x	x	SYM
ejpam-6178	330	15	(	(	PUNCT
ejpam-6178	330	16	a	a	X
ejpam-6178	330	17	)	)	PUNCT
ejpam-6178	330	18	is	be	AUX
ejpam-6178	330	19	open	open	ADJ
ejpam-6178	330	20	in	in	ADP
ejpam-6178	330	21	x	x	PUNCT
ejpam-6178	330	22	by	by	ADP
ejpam-6178	330	23	lemma	lemma	PROPN
ejpam-6178	330	24	2	2	PROPN
ejpam-6178	330	25	(	(	PUNCT
ejpam-6178	330	26	ii	ii	NOUN
ejpam-6178	330	27	)	)	PUNCT
ejpam-6178	330	28	.	.	PUNCT
ejpam-6178	331	1	now	now	ADV
ejpam-6178	331	2	by	by	ADP
ejpam-6178	331	3	db2	db2	PROPN
ejpam-6178	331	4	,	,	PUNCT
ejpam-6178	331	5	x	x	PUNCT
ejpam-6178	331	6	=	=	SYM
ejpam-6178	331	7	1x	1x	NUM
ejpam-6178	331	8	◦	◦	NOUN
ejpam-6178	331	9	x	x	SYM
ejpam-6178	331	10	=	=	SYM
ejpam-6178	331	11	fx(1x	fx(1x	NOUN
ejpam-6178	331	12	)	)	PUNCT
ejpam-6178	331	13	∈	∈	PROPN
ejpam-6178	331	14	a.	a.	NOUN
ejpam-6178	331	15	hence	hence	ADV
ejpam-6178	331	16	,	,	PUNCT
ejpam-6178	331	17	1x	1x	PROPN
ejpam-6178	331	18	∈	∈	PROPN
ejpam-6178	331	19	f−1	f−1	PROPN
ejpam-6178	331	20	x	x	SYM
ejpam-6178	331	21	(	(	PUNCT
ejpam-6178	331	22	a	a	NOUN
ejpam-6178	331	23	)	)	PUNCT
ejpam-6178	331	24	.	.	PUNCT
ejpam-6178	332	1	let	let	VERB
ejpam-6178	332	2	b	b	NOUN
ejpam-6178	332	3	=	=	SYM
ejpam-6178	332	4	f−1	f−1	PROPN
ejpam-6178	332	5	x	x	SYM
ejpam-6178	332	6	(	(	PUNCT
ejpam-6178	332	7	a	a	NOUN
ejpam-6178	332	8	)	)	PUNCT
ejpam-6178	332	9	.	.	PUNCT
ejpam-6178	333	1	by	by	ADP
ejpam-6178	333	2	hypothesis	hypothesis	NOUN
ejpam-6178	333	3	,	,	PUNCT
ejpam-6178	333	4	there	there	PRON
ejpam-6178	333	5	exist	exist	VERB
ejpam-6178	333	6	a	a	DET
ejpam-6178	333	7	neighborhood	neighborhood	NOUN
ejpam-6178	333	8	u	u	NOUN
ejpam-6178	333	9	of	of	ADP
ejpam-6178	333	10	1y	1y	PROPN
ejpam-6178	333	11	in	in	ADP
ejpam-6178	333	12	y	y	PRON
ejpam-6178	333	13	such	such	ADJ
ejpam-6178	333	14	that	that	SCONJ
ejpam-6178	333	15	u	u	PROPN
ejpam-6178	333	16	⊆	⊆	NUM
ejpam-6178	333	17	g(b	g(b	NOUN
ejpam-6178	333	18	)	)	PUNCT
ejpam-6178	333	19	.	.	PUNCT
ejpam-6178	334	1	note	note	VERB
ejpam-6178	334	2	that	that	SCONJ
ejpam-6178	334	3	u	u	PROPN
ejpam-6178	334	4	∗	∗	NOUN
ejpam-6178	334	5	y	y	PROPN
ejpam-6178	334	6	is	be	AUX
ejpam-6178	334	7	open	open	ADJ
ejpam-6178	334	8	in	in	ADP
ejpam-6178	334	9	y	y	PROPN
ejpam-6178	334	10	by	by	ADP
ejpam-6178	334	11	lemma	lemma	PROPN
ejpam-6178	334	12	2	2	PROPN
ejpam-6178	334	13	(	(	PUNCT
ejpam-6178	334	14	i	i	NOUN
ejpam-6178	334	15	)	)	PUNCT
ejpam-6178	334	16	.	.	PUNCT
ejpam-6178	335	1	by	by	ADP
ejpam-6178	335	2	db2	db2	PROPN
ejpam-6178	335	3	,	,	PUNCT
ejpam-6178	335	4	y	y	PROPN
ejpam-6178	335	5	=	=	SYM
ejpam-6178	335	6	1y	1y	PROPN
ejpam-6178	335	7	∗	∗	X
ejpam-6178	335	8	y	y	PROPN
ejpam-6178	335	9	∈	∈	PROPN
ejpam-6178	335	10	u	u	PROPN
ejpam-6178	335	11	∗	∗	NOUN
ejpam-6178	335	12	y.	y.	PROPN
ejpam-6178	335	13	let	let	VERB
ejpam-6178	335	14	u	u	PROPN
ejpam-6178	335	15	∈	∈	PROPN
ejpam-6178	335	16	b.	b.	PROPN
ejpam-6178	335	17	then	then	ADV
ejpam-6178	335	18	u	u	X
ejpam-6178	335	19	◦	◦	NOUN
ejpam-6178	335	20	x	x	X
ejpam-6178	335	21	∈	∈	PROPN
ejpam-6178	335	22	b	b	X
ejpam-6178	335	23	◦	◦	NOUN
ejpam-6178	335	24	x	x	NOUN
ejpam-6178	335	25	,	,	PUNCT
ejpam-6178	335	26	u	u	NOUN
ejpam-6178	335	27	◦	◦	NOUN
ejpam-6178	335	28	x	x	X
ejpam-6178	335	29	=	=	SYM
ejpam-6178	335	30	fx(u	fx(u	X
ejpam-6178	335	31	)	)	PUNCT
ejpam-6178	335	32	∈	∈	PROPN
ejpam-6178	335	33	a.	a.	NOUN
ejpam-6178	335	34	hence	hence	ADV
ejpam-6178	335	35	,	,	PUNCT
ejpam-6178	335	36	b	b	X
ejpam-6178	336	1	◦	◦	NOUN
ejpam-6178	336	2	x	x	SYM
ejpam-6178	336	3	⊆	⊆	NUM
ejpam-6178	336	4	a.	a.	NOUN
ejpam-6178	336	5	then	then	ADV
ejpam-6178	336	6	,	,	PUNCT
ejpam-6178	336	7	g(b	g(b	PROPN
ejpam-6178	336	8	◦	◦	PROPN
ejpam-6178	336	9	x	x	NOUN
ejpam-6178	336	10	)	)	PUNCT
ejpam-6178	336	11	⊆	⊆	NUM
ejpam-6178	336	12	g(a	g(a	PROPN
ejpam-6178	336	13	)	)	PUNCT
ejpam-6178	336	14	.	.	PUNCT
ejpam-6178	337	1	now	now	ADV
ejpam-6178	337	2	,	,	PUNCT
ejpam-6178	337	3	u	u	NOUN
ejpam-6178	337	4	∗y	∗y	PROPN
ejpam-6178	337	5	=	=	SYM
ejpam-6178	337	6	u	u	PROPN
ejpam-6178	337	7	∗g(x	∗g(x	NOUN
ejpam-6178	337	8	)	)	PUNCT
ejpam-6178	337	9	⊆	⊆	NUM
ejpam-6178	337	10	g(b)∗g(x	g(b)∗g(x	NOUN
ejpam-6178	337	11	)	)	PUNCT
ejpam-6178	337	12	=	=	SYM
ejpam-6178	338	1	g(b	g(b	PROPN
ejpam-6178	338	2	◦	◦	PROPN
ejpam-6178	338	3	x	x	NOUN
ejpam-6178	338	4	)	)	PUNCT
ejpam-6178	338	5	⊆	⊆	NUM
ejpam-6178	338	6	g(a	g(a	PROPN
ejpam-6178	338	7	)	)	PUNCT
ejpam-6178	338	8	.	.	PUNCT
ejpam-6178	339	1	therefore	therefore	ADV
ejpam-6178	339	2	,	,	PUNCT
ejpam-6178	339	3	for	for	ADP
ejpam-6178	339	4	all	all	DET
ejpam-6178	339	5	y	y	PROPN
ejpam-6178	339	6	∈	∈	PROPN
ejpam-6178	339	7	g(a	g(a	PROPN
ejpam-6178	339	8	)	)	PUNCT
ejpam-6178	339	9	,	,	PUNCT
ejpam-6178	339	10	there	there	PRON
ejpam-6178	339	11	exists	exist	VERB
ejpam-6178	339	12	a	a	DET
ejpam-6178	339	13	neighborhood	neighborhood	NOUN
ejpam-6178	339	14	u	u	NOUN
ejpam-6178	339	15	∗	∗	NOUN
ejpam-6178	339	16	y	y	PROPN
ejpam-6178	339	17	of	of	ADP
ejpam-6178	339	18	y	y	PROPN
ejpam-6178	339	19	in	in	ADP
ejpam-6178	339	20	y	y	PROPN
ejpam-6178	339	21	such	such	ADJ
ejpam-6178	339	22	that	that	SCONJ
ejpam-6178	339	23	u	u	PROPN
ejpam-6178	339	24	∗	∗	NOUN
ejpam-6178	339	25	y	y	PROPN
ejpam-6178	339	26	⊆	⊆	NUM
ejpam-6178	339	27	g(a	g(a	PROPN
ejpam-6178	339	28	)	)	PUNCT
ejpam-6178	339	29	.	.	PUNCT
ejpam-6178	340	1	by	by	ADP
ejpam-6178	340	2	remark	remark	NOUN
ejpam-6178	340	3	2	2	NUM
ejpam-6178	340	4	,	,	PUNCT
ejpam-6178	340	5	g(a	g(a	PROPN
ejpam-6178	340	6	)	)	PUNCT
ejpam-6178	340	7	is	be	AUX
ejpam-6178	340	8	open	open	ADJ
ejpam-6178	340	9	in	in	ADP
ejpam-6178	340	10	y	y	PROPN
ejpam-6178	340	11	.	.	PUNCT
ejpam-6178	341	1	hence	hence	ADV
ejpam-6178	341	2	,	,	PUNCT
ejpam-6178	341	3	g	g	PROPN
ejpam-6178	341	4	is	be	AUX
ejpam-6178	341	5	an	an	DET
ejpam-6178	341	6	open	open	ADJ
ejpam-6178	341	7	mapping	mapping	NOUN
ejpam-6178	341	8	.	.	PUNCT
ejpam-6178	342	1	definition	definition	NOUN
ejpam-6178	342	2	15	15	NUM
ejpam-6178	342	3	.	.	PUNCT
ejpam-6178	343	1	let	let	VERB
ejpam-6178	343	2	(	(	PUNCT
ejpam-6178	343	3	x	x	NOUN
ejpam-6178	343	4	,	,	PUNCT
ejpam-6178	343	5	◦	◦	NOUN
ejpam-6178	343	6	,	,	PUNCT
ejpam-6178	343	7	τ	τ	X
ejpam-6178	343	8	)	)	PUNCT
ejpam-6178	343	9	and	and	CCONJ
ejpam-6178	343	10	(	(	PUNCT
ejpam-6178	343	11	y	y	PROPN
ejpam-6178	343	12	,	,	PUNCT
ejpam-6178	343	13	∗	∗	NOUN
ejpam-6178	343	14	,	,	PUNCT
ejpam-6178	343	15	τ∗	τ∗	NOUN
ejpam-6178	343	16	)	)	PUNCT
ejpam-6178	343	17	be	be	VERB
ejpam-6178	343	18	tdb	tdb	NOUN
ejpam-6178	343	19	-	-	PUNCT
ejpam-6178	343	20	algebras	algebras	X
ejpam-6178	343	21	.	.	PUNCT
ejpam-6178	344	1	a	a	DET
ejpam-6178	344	2	mapping	mapping	NOUN
ejpam-6178	344	3	φ	φ	NOUN
ejpam-6178	344	4	:	:	PUNCT
ejpam-6178	344	5	x	x	X
ejpam-6178	344	6	→	→	SYM
ejpam-6178	344	7	y	y	PROPN
ejpam-6178	344	8	is	be	AUX
ejpam-6178	344	9	called	call	VERB
ejpam-6178	344	10	a	a	DET
ejpam-6178	344	11	topological	topological	ADJ
ejpam-6178	344	12	dual	dual	ADJ
ejpam-6178	344	13	b	b	NOUN
ejpam-6178	344	14	-	-	PUNCT
ejpam-6178	344	15	isomorphism	isomorphism	NOUN
ejpam-6178	344	16	(	(	PUNCT
ejpam-6178	344	17	or	or	CCONJ
ejpam-6178	344	18	tdbisomorphism	tdbisomorphism	NOUN
ejpam-6178	344	19	)	)	PUNCT
ejpam-6178	344	20	if	if	SCONJ
ejpam-6178	344	21	(	(	PUNCT
ejpam-6178	344	22	i	i	NOUN
ejpam-6178	344	23	)	)	PUNCT
ejpam-6178	344	24	φ	φ	PROPN
ejpam-6178	344	25	is	be	AUX
ejpam-6178	344	26	a	a	DET
ejpam-6178	344	27	db	db	NOUN
ejpam-6178	344	28	-	-	PUNCT
ejpam-6178	344	29	isomorphism	isomorphism	NOUN
ejpam-6178	344	30	from	from	ADP
ejpam-6178	344	31	(	(	PUNCT
ejpam-6178	344	32	x	x	NOUN
ejpam-6178	344	33	,	,	PUNCT
ejpam-6178	344	34	◦	◦	NOUN
ejpam-6178	344	35	,	,	PUNCT
ejpam-6178	344	36	1x	1x	NUM
ejpam-6178	344	37	)	)	PUNCT
ejpam-6178	344	38	to	to	ADP
ejpam-6178	344	39	(	(	PUNCT
ejpam-6178	344	40	y	y	PROPN
ejpam-6178	344	41	,	,	PUNCT
ejpam-6178	344	42	∗	∗	NOUN
ejpam-6178	344	43	,	,	PUNCT
ejpam-6178	344	44	1y	1y	NOUN
ejpam-6178	344	45	)	)	PUNCT
ejpam-6178	344	46	,	,	PUNCT
ejpam-6178	344	47	and	and	CCONJ
ejpam-6178	344	48	(	(	PUNCT
ejpam-6178	344	49	ii	ii	NOUN
ejpam-6178	344	50	)	)	PUNCT
ejpam-6178	344	51	φ	φ	PROPN
ejpam-6178	344	52	is	be	AUX
ejpam-6178	344	53	continuous	continuous	ADJ
ejpam-6178	344	54	and	and	CCONJ
ejpam-6178	344	55	open	open	ADJ
ejpam-6178	344	56	from	from	ADP
ejpam-6178	344	57	(	(	PUNCT
ejpam-6178	344	58	x	x	NOUN
ejpam-6178	344	59	,	,	PUNCT
ejpam-6178	344	60	τ	τ	X
ejpam-6178	344	61	)	)	PUNCT
ejpam-6178	344	62	to	to	ADP
ejpam-6178	344	63	(	(	PUNCT
ejpam-6178	344	64	y	y	NOUN
ejpam-6178	344	65	,	,	PUNCT
ejpam-6178	344	66	τ∗	τ∗	NOUN
ejpam-6178	344	67	)	)	PUNCT
ejpam-6178	344	68	.	.	PUNCT
ejpam-6178	345	1	in	in	ADP
ejpam-6178	345	2	definition	definition	NOUN
ejpam-6178	345	3	15	15	NUM
ejpam-6178	345	4	,	,	PUNCT
ejpam-6178	345	5	if	if	SCONJ
ejpam-6178	345	6	the	the	DET
ejpam-6178	345	7	map	map	NOUN
ejpam-6178	345	8	from	from	ADP
ejpam-6178	345	9	x	x	PUNCT
ejpam-6178	345	10	to	to	ADP
ejpam-6178	345	11	y	y	PROPN
ejpam-6178	345	12	satisfies	satisfy	VERB
ejpam-6178	345	13	the	the	DET
ejpam-6178	345	14	two	two	NUM
ejpam-6178	345	15	conditions	condition	NOUN
ejpam-6178	345	16	,	,	PUNCT
ejpam-6178	345	17	then	then	ADV
ejpam-6178	345	18	x	x	PUNCT
ejpam-6178	345	19	is	be	AUX
ejpam-6178	345	20	topologically	topologically	ADV
ejpam-6178	345	21	isomorphic	isomorphic	ADJ
ejpam-6178	345	22	with	with	ADP
ejpam-6178	345	23	y	y	PROPN
ejpam-6178	345	24	.	.	PUNCT
ejpam-6178	346	1	that	that	PRON
ejpam-6178	346	2	is	be	AUX
ejpam-6178	346	3	,	,	PUNCT
ejpam-6178	346	4	x	x	X
ejpam-6178	346	5	is	be	AUX
ejpam-6178	346	6	isomorphic	isomorphic	ADJ
ejpam-6178	346	7	with	with	ADP
ejpam-6178	346	8	respect	respect	NOUN
ejpam-6178	346	9	to	to	ADP
ejpam-6178	346	10	the	the	DET
ejpam-6178	346	11	underlying	underlie	VERB
ejpam-6178	346	12	algebraic	algebraic	ADJ
ejpam-6178	346	13	structures	structure	NOUN
ejpam-6178	346	14	and	and	CCONJ
ejpam-6178	346	15	at	at	ADP
ejpam-6178	346	16	the	the	DET
ejpam-6178	346	17	same	same	ADJ
ejpam-6178	346	18	time	time	NOUN
ejpam-6178	346	19	homeomorphic	homeomorphic	ADJ
ejpam-6178	346	20	with	with	ADP
ejpam-6178	346	21	respect	respect	NOUN
ejpam-6178	346	22	to	to	ADP
ejpam-6178	346	23	the	the	DET
ejpam-6178	346	24	underlying	underlying	ADJ
ejpam-6178	346	25	topological	topological	ADJ
ejpam-6178	346	26	structures	structure	NOUN
ejpam-6178	346	27	.	.	PUNCT
ejpam-6178	347	1	hence	hence	ADV
ejpam-6178	347	2	,	,	PUNCT
ejpam-6178	347	3	isomorphic	isomorphic	ADJ
ejpam-6178	347	4	tdb	tdb	PROPN
ejpam-6178	347	5	-	-	PUNCT
ejpam-6178	347	6	algebras	algebras	PROPN
ejpam-6178	347	7	means	mean	VERB
ejpam-6178	347	8	that	that	SCONJ
ejpam-6178	347	9	there	there	PRON
ejpam-6178	347	10	exists	exist	VERB
ejpam-6178	347	11	a	a	DET
ejpam-6178	347	12	bijective	bijective	ADJ
ejpam-6178	347	13	map	map	NOUN
ejpam-6178	347	14	that	that	PRON
ejpam-6178	347	15	preserves	preserve	VERB
ejpam-6178	347	16	the	the	DET
ejpam-6178	347	17	underlying	underlie	VERB
ejpam-6178	347	18	algebraic	algebraic	ADJ
ejpam-6178	347	19	structures	structure	NOUN
ejpam-6178	347	20	.	.	PUNCT
ejpam-6178	348	1	moreover	moreover	ADV
ejpam-6178	348	2	,	,	PUNCT
ejpam-6178	348	3	homeomorphic	homeomorphic	ADJ
ejpam-6178	348	4	tdbalgebras	tdbalgebra	NOUN
ejpam-6178	348	5	means	mean	VERB
ejpam-6178	348	6	that	that	SCONJ
ejpam-6178	348	7	there	there	PRON
ejpam-6178	348	8	exists	exist	VERB
ejpam-6178	348	9	a	a	DET
ejpam-6178	348	10	map	map	NOUN
ejpam-6178	348	11	that	that	PRON
ejpam-6178	348	12	is	be	AUX
ejpam-6178	348	13	continuous	continuous	ADJ
ejpam-6178	348	14	and	and	CCONJ
ejpam-6178	348	15	open	open	ADJ
ejpam-6178	348	16	(	(	PUNCT
ejpam-6178	348	17	given	give	VERB
ejpam-6178	348	18	that	that	SCONJ
ejpam-6178	348	19	the	the	DET
ejpam-6178	348	20	map	map	NOUN
ejpam-6178	348	21	is	be	AUX
ejpam-6178	348	22	bijective	bijective	ADJ
ejpam-6178	348	23	)	)	PUNCT
ejpam-6178	348	24	between	between	ADP
ejpam-6178	348	25	the	the	DET
ejpam-6178	348	26	topological	topological	ADJ
ejpam-6178	348	27	spaces	space	NOUN
ejpam-6178	348	28	.	.	PUNCT
ejpam-6178	349	1	we	we	PRON
ejpam-6178	349	2	note	note	VERB
ejpam-6178	349	3	that	that	SCONJ
ejpam-6178	349	4	the	the	DET
ejpam-6178	349	5	relationship	relationship	NOUN
ejpam-6178	349	6	of	of	ADP
ejpam-6178	349	7	open	open	ADJ
ejpam-6178	349	8	maps	map	NOUN
ejpam-6178	349	9	and	and	CCONJ
ejpam-6178	349	10	continuous	continuous	ADJ
ejpam-6178	349	11	maps	map	NOUN
ejpam-6178	349	12	from	from	ADP
ejpam-6178	349	13	the	the	DET
ejpam-6178	349	14	topological	topological	ADJ
ejpam-6178	349	15	spaces	space	NOUN
ejpam-6178	349	16	is	be	AUX
ejpam-6178	349	17	independent	independent	ADJ
ejpam-6178	349	18	.	.	PUNCT
ejpam-6178	350	1	even	even	ADV
ejpam-6178	350	2	if	if	SCONJ
ejpam-6178	350	3	the	the	DET
ejpam-6178	350	4	map	map	NOUN
ejpam-6178	350	5	is	be	AUX
ejpam-6178	350	6	bijective	bijective	ADJ
ejpam-6178	350	7	and	and	CCONJ
ejpam-6178	350	8	continuous	continuous	ADJ
ejpam-6178	350	9	,	,	PUNCT
ejpam-6178	350	10	open	open	ADJ
ejpam-6178	350	11	map	map	NOUN
ejpam-6178	350	12	is	be	AUX
ejpam-6178	350	13	not	not	PART
ejpam-6178	350	14	guaranteed	guarantee	VERB
ejpam-6178	350	15	.	.	PUNCT
ejpam-6178	351	1	thus	thus	ADV
ejpam-6178	351	2	,	,	PUNCT
ejpam-6178	351	3	in	in	ADP
ejpam-6178	351	4	definition	definition	NOUN
ejpam-6178	351	5	15	15	NUM
ejpam-6178	351	6	a	a	DET
ejpam-6178	351	7	tdb	tdb	NOUN
ejpam-6178	351	8	-	-	NOUN
ejpam-6178	351	9	homomorphism	homomorphism	NOUN
ejpam-6178	351	10	that	that	PRON
ejpam-6178	351	11	is	be	AUX
ejpam-6178	351	12	bijective	bijective	ADJ
ejpam-6178	351	13	is	be	AUX
ejpam-6178	351	14	not	not	PART
ejpam-6178	351	15	necessarily	necessarily	ADV
ejpam-6178	351	16	a	a	DET
ejpam-6178	351	17	tdb	tdb	PROPN
ejpam-6178	351	18	-	-	PUNCT
ejpam-6178	351	19	isomorphism	isomorphism	NOUN
ejpam-6178	351	20	.	.	PUNCT
ejpam-6178	352	1	but	but	CCONJ
ejpam-6178	352	2	a	a	DET
ejpam-6178	352	3	tdb	tdb	PROPN
ejpam-6178	352	4	-	-	PUNCT
ejpam-6178	352	5	isomorphism	isomorphism	NOUN
ejpam-6178	352	6	map	map	NOUN
ejpam-6178	352	7	is	be	AUX
ejpam-6178	352	8	a	a	DET
ejpam-6178	352	9	tdb	tdb	PROPN
ejpam-6178	352	10	-	-	PUNCT
ejpam-6178	352	11	homomorphism	homomorphism	NOUN
ejpam-6178	352	12	map	map	NOUN
ejpam-6178	352	13	.	.	PUNCT
ejpam-6178	352	14	example	example	NOUN
ejpam-6178	352	15	7	7	NUM
ejpam-6178	352	16	.	.	X
ejpam-6178	352	17	consider	consider	VERB
ejpam-6178	352	18	example	example	NOUN
ejpam-6178	352	19	5	5	NUM
ejpam-6178	352	20	and	and	CCONJ
ejpam-6178	352	21	example	example	NOUN
ejpam-6178	352	22	6	6	NUM
ejpam-6178	352	23	,	,	PUNCT
ejpam-6178	352	24	φ	φ	PROPN
ejpam-6178	352	25	is	be	AUX
ejpam-6178	352	26	a	a	DET
ejpam-6178	352	27	db	db	NOUN
ejpam-6178	352	28	-	-	PUNCT
ejpam-6178	352	29	isomorphism	isomorphism	NOUN
ejpam-6178	352	30	,	,	PUNCT
ejpam-6178	352	31	and	and	CCONJ
ejpam-6178	352	32	φ	φ	PROPN
ejpam-6178	352	33	is	be	AUX
ejpam-6178	352	34	a	a	DET
ejpam-6178	352	35	continuous	continuous	ADJ
ejpam-6178	352	36	and	and	CCONJ
ejpam-6178	352	37	open	open	ADJ
ejpam-6178	352	38	mapping	mapping	NOUN
ejpam-6178	352	39	from	from	ADP
ejpam-6178	352	40	(	(	PUNCT
ejpam-6178	352	41	x	x	NOUN
ejpam-6178	352	42	,	,	PUNCT
ejpam-6178	352	43	τ	τ	X
ejpam-6178	352	44	)	)	PUNCT
ejpam-6178	352	45	to	to	ADP
ejpam-6178	352	46	(	(	PUNCT
ejpam-6178	352	47	x	x	X
ejpam-6178	352	48	,	,	PUNCT
ejpam-6178	352	49	τ	τ	PROPN
ejpam-6178	352	50	)	)	PUNCT
ejpam-6178	352	51	.	.	PUNCT
ejpam-6178	353	1	hence	hence	ADV
ejpam-6178	353	2	,	,	PUNCT
ejpam-6178	353	3	φ	φ	PROPN
ejpam-6178	353	4	is	be	AUX
ejpam-6178	353	5	a	a	DET
ejpam-6178	353	6	tdb	tdb	PROPN
ejpam-6178	353	7	-	-	PUNCT
ejpam-6178	353	8	isomorphism	isomorphism	NOUN
ejpam-6178	353	9	.	.	PUNCT
ejpam-6178	354	1	the	the	DET
ejpam-6178	354	2	next	next	ADJ
ejpam-6178	354	3	corollary	corollary	NOUN
ejpam-6178	354	4	is	be	AUX
ejpam-6178	354	5	an	an	DET
ejpam-6178	354	6	immediate	immediate	ADJ
ejpam-6178	354	7	result	result	NOUN
ejpam-6178	354	8	from	from	ADP
ejpam-6178	354	9	theorem	theorem	ADJ
ejpam-6178	354	10	16	16	NUM
ejpam-6178	354	11	.	.	PUNCT
ejpam-6178	355	1	corollary	corollary	ADJ
ejpam-6178	355	2	4	4	NUM
ejpam-6178	355	3	.	.	PUNCT
ejpam-6178	356	1	let	let	VERB
ejpam-6178	356	2	x	x	PRON
ejpam-6178	356	3	and	and	CCONJ
ejpam-6178	356	4	y	y	PROPN
ejpam-6178	356	5	be	be	AUX
ejpam-6178	356	6	transitive	transitive	ADJ
ejpam-6178	356	7	open	open	ADJ
ejpam-6178	356	8	tdb	tdb	NOUN
ejpam-6178	356	9	-	-	PUNCT
ejpam-6178	356	10	algebras	algebras	PROPN
ejpam-6178	356	11	and	and	CCONJ
ejpam-6178	356	12	g	g	PROPN
ejpam-6178	356	13	a	a	DET
ejpam-6178	356	14	db	db	NOUN
ejpam-6178	356	15	-	-	PUNCT
ejpam-6178	356	16	isomorphism	isomorphism	NOUN
ejpam-6178	356	17	from	from	ADP
ejpam-6178	356	18	(	(	PUNCT
ejpam-6178	356	19	x	x	NOUN
ejpam-6178	356	20	,	,	PUNCT
ejpam-6178	356	21	◦	◦	NOUN
ejpam-6178	356	22	,	,	PUNCT
ejpam-6178	356	23	1x	1x	NUM
ejpam-6178	356	24	)	)	PUNCT
ejpam-6178	356	25	to	to	ADP
ejpam-6178	356	26	(	(	PUNCT
ejpam-6178	356	27	y	y	PROPN
ejpam-6178	356	28	,	,	PUNCT
ejpam-6178	356	29	∗	∗	NOUN
ejpam-6178	356	30	,	,	PUNCT
ejpam-6178	356	31	1y	1y	NOUN
ejpam-6178	356	32	)	)	PUNCT
ejpam-6178	356	33	.	.	PUNCT
ejpam-6178	357	1	if	if	SCONJ
ejpam-6178	357	2	for	for	ADP
ejpam-6178	357	3	each	each	DET
ejpam-6178	357	4	neighborhood	neighborhood	NOUN
ejpam-6178	357	5	u	u	NOUN
ejpam-6178	357	6	of	of	ADP
ejpam-6178	357	7	1y	1y	PROPN
ejpam-6178	357	8	in	in	ADP
ejpam-6178	357	9	y	y	PROPN
ejpam-6178	357	10	,	,	PUNCT
ejpam-6178	357	11	there	there	PRON
ejpam-6178	357	12	exists	exist	VERB
ejpam-6178	357	13	a	a	DET
ejpam-6178	357	14	neighborhood	neighborhood	NOUN
ejpam-6178	357	15	of	of	ADP
ejpam-6178	357	16	v	v	NOUN
ejpam-6178	357	17	of	of	ADP
ejpam-6178	357	18	1x	1x	NUM
ejpam-6178	357	19	in	in	ADP
ejpam-6178	357	20	x	x	PUNCT
ejpam-6178	357	21	such	such	ADJ
ejpam-6178	357	22	that	that	SCONJ
ejpam-6178	357	23	g(v	g(v	PROPN
ejpam-6178	357	24	)	)	PUNCT
ejpam-6178	357	25	⊆	⊆	NUM
ejpam-6178	357	26	u	u	NOUN
ejpam-6178	357	27	and	and	CCONJ
ejpam-6178	357	28	if	if	SCONJ
ejpam-6178	357	29	for	for	ADP
ejpam-6178	357	30	each	each	DET
ejpam-6178	357	31	neighborhood	neighborhood	NOUN
ejpam-6178	357	32	of	of	ADP
ejpam-6178	357	33	v	v	NOUN
ejpam-6178	357	34	of	of	ADP
ejpam-6178	357	35	1x	1x	NUM
ejpam-6178	357	36	in	in	ADP
ejpam-6178	357	37	x	x	NOUN
ejpam-6178	357	38	,	,	PUNCT
ejpam-6178	357	39	there	there	PRON
ejpam-6178	357	40	exists	exist	VERB
ejpam-6178	357	41	a	a	DET
ejpam-6178	357	42	neighborhood	neighborhood	NOUN
ejpam-6178	357	43	u	u	NOUN
ejpam-6178	357	44	of	of	ADP
ejpam-6178	357	45	1y	1y	PROPN
ejpam-6178	357	46	in	in	ADP
ejpam-6178	357	47	y	y	PRON
ejpam-6178	357	48	such	such	ADJ
ejpam-6178	357	49	that	that	SCONJ
ejpam-6178	357	50	y	y	PROPN
ejpam-6178	357	51	⊆	⊆	NUM
ejpam-6178	357	52	g(v	g(v	PROPN
ejpam-6178	357	53	)	)	PUNCT
ejpam-6178	357	54	,	,	PUNCT
ejpam-6178	357	55	then	then	ADV
ejpam-6178	357	56	g	g	PROPN
ejpam-6178	357	57	is	be	AUX
ejpam-6178	357	58	a	a	DET
ejpam-6178	357	59	tdb	tdb	PROPN
ejpam-6178	357	60	-	-	PUNCT
ejpam-6178	357	61	isomorphism	isomorphism	NOUN
ejpam-6178	357	62	.	.	PUNCT
ejpam-6178	358	1	in	in	ADP
ejpam-6178	358	2	theorem	theorem	ADJ
ejpam-6178	358	3	14	14	NUM
ejpam-6178	358	4	(	(	PUNCT
ejpam-6178	358	5	ii	ii	NOUN
ejpam-6178	358	6	)	)	PUNCT
ejpam-6178	358	7	,	,	PUNCT
ejpam-6178	358	8	a	a	DET
ejpam-6178	358	9	subset	subset	NOUN
ejpam-6178	358	10	s	s	NOUN
ejpam-6178	358	11	of	of	ADP
ejpam-6178	358	12	a	a	DET
ejpam-6178	358	13	tdb	tdb	NOUN
ejpam-6178	358	14	-	-	NOUN
ejpam-6178	358	15	algebra	algebra	NOUN
ejpam-6178	358	16	should	should	AUX
ejpam-6178	358	17	be	be	AUX
ejpam-6178	358	18	open	open	ADJ
ejpam-6178	358	19	to	to	PART
ejpam-6178	358	20	imply	imply	VERB
ejpam-6178	358	21	that	that	SCONJ
ejpam-6178	358	22	the	the	DET
ejpam-6178	358	23	natural	natural	ADJ
ejpam-6178	358	24	db	db	NOUN
ejpam-6178	358	25	-	-	PUNCT
ejpam-6178	358	26	homomorphism	homomorphism	NOUN
ejpam-6178	358	27	is	be	AUX
ejpam-6178	358	28	an	an	DET
ejpam-6178	358	29	open	open	ADJ
ejpam-6178	358	30	tdb	tdb	NOUN
ejpam-6178	358	31	-	-	NOUN
ejpam-6178	358	32	homomorphism	homomorphism	NOUN
ejpam-6178	358	33	that	that	PRON
ejpam-6178	358	34	is	be	AUX
ejpam-6178	358	35	,	,	PUNCT
ejpam-6178	358	36	the	the	DET
ejpam-6178	358	37	natural	natural	ADJ
ejpam-6178	358	38	db	db	NOUN
ejpam-6178	358	39	-	-	PUNCT
ejpam-6178	358	40	homomorphism	homomorphism	NOUN
ejpam-6178	358	41	is	be	AUX
ejpam-6178	358	42	an	an	DET
ejpam-6178	358	43	open	open	ADJ
ejpam-6178	358	44	and	and	CCONJ
ejpam-6178	358	45	continuous	continuous	ADJ
ejpam-6178	358	46	map	map	NOUN
ejpam-6178	358	47	.	.	PUNCT
ejpam-6178	359	1	now	now	ADV
ejpam-6178	359	2	in	in	ADP
ejpam-6178	359	3	terms	term	NOUN
ejpam-6178	359	4	of	of	ADP
ejpam-6178	359	5	mapping	mapping	NOUN
ejpam-6178	359	6	from	from	ADP
ejpam-6178	359	7	a	a	DET
ejpam-6178	359	8	dual	dual	ADJ
ejpam-6178	359	9	b	b	NOUN
ejpam-6178	359	10	-	-	PUNCT
ejpam-6178	359	11	algebra	algebra	NOUN
ejpam-6178	359	12	to	to	ADP
ejpam-6178	359	13	a	a	DET
ejpam-6178	359	14	quotient	quotient	NOUN
ejpam-6178	359	15	db	db	NOUN
ejpam-6178	359	16	-	-	PUNCT
ejpam-6178	359	17	algebra	algebra	NOUN
ejpam-6178	359	18	,	,	PUNCT
ejpam-6178	359	19	the	the	DET
ejpam-6178	359	20	natural	natural	ADJ
ejpam-6178	359	21	db	db	NOUN
ejpam-6178	359	22	-	-	PUNCT
ejpam-6178	359	23	homomorphism	homomorphism	NOUN
ejpam-6178	359	24	is	be	AUX
ejpam-6178	359	25	surjective	surjective	ADJ
ejpam-6178	359	26	by	by	ADP
ejpam-6178	359	27	theorem	theorem	NOUN
ejpam-6178	359	28	4	4	NUM
ejpam-6178	359	29	and	and	CCONJ
ejpam-6178	359	30	in	in	ADP
ejpam-6178	359	31	general	general	ADJ
ejpam-6178	359	32	,	,	PUNCT
ejpam-6178	359	33	it	it	PRON
ejpam-6178	359	34	is	be	AUX
ejpam-6178	359	35	not	not	PART
ejpam-6178	359	36	a	a	DET
ejpam-6178	359	37	one	one	NUM
ejpam-6178	359	38	-	-	PUNCT
ejpam-6178	359	39	to	to	ADP
ejpam-6178	359	40	-	-	PUNCT
ejpam-6178	359	41	one	one	NUM
ejpam-6178	359	42	mapping	mapping	NOUN
ejpam-6178	359	43	.	.	PUNCT
ejpam-6178	360	1	if	if	SCONJ
ejpam-6178	360	2	the	the	DET
ejpam-6178	360	3	natural	natural	ADJ
ejpam-6178	360	4	db	db	NOUN
ejpam-6178	360	5	-	-	PUNCT
ejpam-6178	360	6	homomorphism	homomorphism	NOUN
ejpam-6178	360	7	is	be	AUX
ejpam-6178	360	8	one	one	NUM
ejpam-6178	360	9	-	-	PUNCT
ejpam-6178	360	10	to	to	ADP
ejpam-6178	360	11	-	-	PUNCT
ejpam-6178	360	12	one	one	NUM
ejpam-6178	360	13	,	,	PUNCT
ejpam-6178	360	14	then	then	ADV
ejpam-6178	360	15	it	it	PRON
ejpam-6178	360	16	is	be	AUX
ejpam-6178	360	17	a	a	DET
ejpam-6178	360	18	tdb	tdb	NOUN
ejpam-6178	360	19	-	-	NOUN
ejpam-6178	360	20	isomorphism	isomorphism	NOUN
ejpam-6178	360	21	by	by	ADP
ejpam-6178	360	22	definition	definition	NOUN
ejpam-6178	360	23	15	15	NUM
ejpam-6178	360	24	.	.	PUNCT
ejpam-6178	361	1	hence	hence	ADV
ejpam-6178	361	2	,	,	PUNCT
ejpam-6178	361	3	with	with	ADP
ejpam-6178	361	4	theorem	theorem	ADJ
ejpam-6178	361	5	14	14	NUM
ejpam-6178	361	6	(	(	PUNCT
ejpam-6178	361	7	ii	ii	NOUN
ejpam-6178	361	8	)	)	PUNCT
ejpam-6178	361	9	such	such	ADJ
ejpam-6178	361	10	that	that	SCONJ
ejpam-6178	361	11	the	the	DET
ejpam-6178	361	12	natural	natural	ADJ
ejpam-6178	361	13	db	db	NOUN
ejpam-6178	361	14	-	-	PUNCT
ejpam-6178	361	15	homomorphism	homomorphism	NOUN
ejpam-6178	361	16	is	be	AUX
ejpam-6178	361	17	bijective	bijective	ADJ
ejpam-6178	361	18	,	,	PUNCT
ejpam-6178	361	19	the	the	DET
ejpam-6178	361	20	next	next	ADJ
ejpam-6178	361	21	corollary	corollary	NOUN
ejpam-6178	361	22	is	be	AUX
ejpam-6178	361	23	presented	present	VERB
ejpam-6178	361	24	.	.	PUNCT
ejpam-6178	362	1	r.	r.	PROPN
ejpam-6178	362	2	nuñez	nuñez	PROPN
ejpam-6178	362	3	,	,	PUNCT
ejpam-6178	362	4	k.	k.	PROPN
ejpam-6178	362	5	b.	b.	PROPN
ejpam-6178	362	6	fuentes	fuentes	PROPN
ejpam-6178	362	7	/	/	SYM
ejpam-6178	362	8	eur	eur	PROPN
ejpam-6178	362	9	.	.	PUNCT
ejpam-6178	363	1	j.	j.	PROPN
ejpam-6178	363	2	pure	pure	PROPN
ejpam-6178	363	3	appl	appl	PROPN
ejpam-6178	363	4	.	.	PROPN
ejpam-6178	363	5	math	math	PROPN
ejpam-6178	363	6	,	,	PUNCT
ejpam-6178	363	7	18	18	NUM
ejpam-6178	363	8	(	(	PUNCT
ejpam-6178	363	9	4	4	NUM
ejpam-6178	363	10	)	)	PUNCT
ejpam-6178	363	11	(	(	PUNCT
ejpam-6178	363	12	2025	2025	NUM
ejpam-6178	363	13	)	)	PUNCT
ejpam-6178	363	14	,	,	PUNCT
ejpam-6178	363	15	6178	6178	NUM
ejpam-6178	363	16	11	11	NUM
ejpam-6178	363	17	of	of	ADP
ejpam-6178	363	18	15	15	NUM
ejpam-6178	363	19	corollary	corollary	ADJ
ejpam-6178	363	20	5	5	NUM
ejpam-6178	363	21	.	.	PUNCT
ejpam-6178	364	1	let	let	VERB
ejpam-6178	364	2	(	(	PUNCT
ejpam-6178	364	3	x	x	NOUN
ejpam-6178	364	4	,	,	PUNCT
ejpam-6178	364	5	◦	◦	NOUN
ejpam-6178	364	6	,	,	PUNCT
ejpam-6178	364	7	τ	τ	X
ejpam-6178	364	8	)	)	PUNCT
ejpam-6178	364	9	be	be	VERB
ejpam-6178	364	10	a	a	DET
ejpam-6178	364	11	tdb	tdb	NOUN
ejpam-6178	364	12	algebra	algebra	NOUN
ejpam-6178	364	13	and	and	CCONJ
ejpam-6178	364	14	s	s	AUX
ejpam-6178	364	15	be	be	AUX
ejpam-6178	364	16	open	open	ADJ
ejpam-6178	364	17	in	in	ADP
ejpam-6178	364	18	x.	x.	NOUN
ejpam-6178	364	19	if	if	SCONJ
ejpam-6178	364	20	the	the	DET
ejpam-6178	364	21	natural	natural	ADJ
ejpam-6178	364	22	dbhomomorphism	dbhomomorphism	NOUN
ejpam-6178	364	23	φ	φ	PROPN
ejpam-6178	364	24	is	be	AUX
ejpam-6178	364	25	bijective	bijective	ADJ
ejpam-6178	364	26	,	,	PUNCT
ejpam-6178	364	27	then	then	ADV
ejpam-6178	364	28	φ	φ	PROPN
ejpam-6178	364	29	is	be	AUX
ejpam-6178	364	30	a	a	DET
ejpam-6178	364	31	tdb	tdb	PROPN
ejpam-6178	364	32	-	-	PUNCT
ejpam-6178	364	33	isomorphism	isomorphism	NOUN
ejpam-6178	364	34	.	.	PUNCT
ejpam-6178	365	1	theorem	theorem	PROPN
ejpam-6178	365	2	17	17	NUM
ejpam-6178	365	3	.	.	PUNCT
ejpam-6178	366	1	let	let	VERB
ejpam-6178	366	2	(	(	PUNCT
ejpam-6178	366	3	x	x	NOUN
ejpam-6178	366	4	,	,	PUNCT
ejpam-6178	366	5	◦	◦	NOUN
ejpam-6178	366	6	,	,	PUNCT
ejpam-6178	366	7	τ	τ	X
ejpam-6178	366	8	)	)	PUNCT
ejpam-6178	366	9	and	and	CCONJ
ejpam-6178	366	10	(	(	PUNCT
ejpam-6178	366	11	y	y	PROPN
ejpam-6178	366	12	,	,	PUNCT
ejpam-6178	366	13	∗	∗	NOUN
ejpam-6178	366	14	,	,	PUNCT
ejpam-6178	366	15	τ	τ	PROPN
ejpam-6178	366	16	′	′	NUM
ejpam-6178	366	17	)	)	PUNCT
ejpam-6178	366	18	be	be	VERB
ejpam-6178	366	19	tdb	tdb	PROPN
ejpam-6178	366	20	-	-	PUNCT
ejpam-6178	366	21	algebras	algebras	PROPN
ejpam-6178	366	22	and	and	CCONJ
ejpam-6178	366	23	g	g	PROPN
ejpam-6178	366	24	is	be	AUX
ejpam-6178	366	25	an	an	DET
ejpam-6178	366	26	open	open	ADJ
ejpam-6178	366	27	tdb	tdb	NOUN
ejpam-6178	366	28	-	-	NOUN
ejpam-6178	366	29	homomorphism	homomorphism	NOUN
ejpam-6178	366	30	from	from	ADP
ejpam-6178	366	31	(	(	PUNCT
ejpam-6178	366	32	x	x	NOUN
ejpam-6178	366	33	,	,	PUNCT
ejpam-6178	366	34	◦	◦	NOUN
ejpam-6178	366	35	,	,	PUNCT
ejpam-6178	366	36	τ	τ	X
ejpam-6178	366	37	)	)	PUNCT
ejpam-6178	366	38	onto	onto	ADP
ejpam-6178	366	39	(	(	PUNCT
ejpam-6178	366	40	y	y	PROPN
ejpam-6178	366	41	,	,	PUNCT
ejpam-6178	366	42	∗	∗	NOUN
ejpam-6178	366	43	,	,	PUNCT
ejpam-6178	366	44	τ	τ	PROPN
ejpam-6178	366	45	′	′	NUM
ejpam-6178	366	46	)	)	PUNCT
ejpam-6178	366	47	with	with	ADP
ejpam-6178	366	48	ker	ker	PROPN
ejpam-6178	366	49	g	g	PROPN
ejpam-6178	366	50	=	=	SYM
ejpam-6178	366	51	s	s	PROPN
ejpam-6178	366	52	and	and	CCONJ
ejpam-6178	366	53	{	{	PUNCT
ejpam-6178	366	54	1y	1y	NOUN
ejpam-6178	366	55	}	}	PUNCT
ejpam-6178	366	56	is	be	AUX
ejpam-6178	366	57	open	open	ADJ
ejpam-6178	366	58	in	in	ADP
ejpam-6178	366	59	y	y	PROPN
ejpam-6178	366	60	.	.	PUNCT
ejpam-6178	367	1	if	if	SCONJ
ejpam-6178	367	2	s	s	PROPN
ejpam-6178	367	3	is	be	AUX
ejpam-6178	367	4	a	a	DET
ejpam-6178	367	5	normal	normal	ADJ
ejpam-6178	367	6	dbsubalgebra	dbsubalgebra	NOUN
ejpam-6178	367	7	of	of	ADP
ejpam-6178	367	8	x	x	PUNCT
ejpam-6178	367	9	and	and	CCONJ
ejpam-6178	367	10	define	define	VERB
ejpam-6178	367	11	f	f	X
ejpam-6178	367	12	:	:	PUNCT
ejpam-6178	367	13	x	x	X
ejpam-6178	367	14	/	/	SYM
ejpam-6178	367	15	s	s	X
ejpam-6178	367	16	→	→	SYM
ejpam-6178	367	17	y	y	PROPN
ejpam-6178	367	18	by	by	ADP
ejpam-6178	367	19	f([a]s	f([a]s	PROPN
ejpam-6178	367	20	)	)	PUNCT
ejpam-6178	367	21	=	=	SYM
ejpam-6178	367	22	g(a	g(a	PROPN
ejpam-6178	367	23	)	)	PUNCT
ejpam-6178	367	24	,	,	PUNCT
ejpam-6178	367	25	then	then	ADV
ejpam-6178	367	26	f	f	PROPN
ejpam-6178	367	27	is	be	AUX
ejpam-6178	367	28	a	a	DET
ejpam-6178	367	29	tdb	tdb	PROPN
ejpam-6178	367	30	-	-	PUNCT
ejpam-6178	367	31	isomorphism	isomorphism	NOUN
ejpam-6178	367	32	.	.	PUNCT
ejpam-6178	368	1	that	that	PRON
ejpam-6178	368	2	is	be	AUX
ejpam-6178	368	3	,	,	PUNCT
ejpam-6178	368	4	x	x	X
ejpam-6178	368	5	/	/	SYM
ejpam-6178	368	6	s	s	VERB
ejpam-6178	368	7	is	be	AUX
ejpam-6178	368	8	topologically	topologically	ADV
ejpam-6178	368	9	isomorphic	isomorphic	ADJ
ejpam-6178	368	10	to	to	ADP
ejpam-6178	368	11	y	y	PROPN
ejpam-6178	368	12	.	.	PUNCT
ejpam-6178	369	1	proof	proof	NOUN
ejpam-6178	369	2	.	.	PUNCT
ejpam-6178	370	1	since	since	SCONJ
ejpam-6178	370	2	g	g	PROPN
ejpam-6178	370	3	is	be	AUX
ejpam-6178	370	4	surjective	surjective	ADJ
ejpam-6178	370	5	,	,	PUNCT
ejpam-6178	370	6	by	by	ADP
ejpam-6178	370	7	remark	remark	NOUN
ejpam-6178	370	8	1	1	NUM
ejpam-6178	370	9	,	,	PUNCT
ejpam-6178	370	10	x	x	X
ejpam-6178	370	11	/	/	SYM
ejpam-6178	370	12	s	s	VERB
ejpam-6178	370	13	∼=	∼=	PROPN
ejpam-6178	370	14	y	y	NOUN
ejpam-6178	370	15	.	.	PUNCT
ejpam-6178	371	1	that	that	PRON
ejpam-6178	371	2	is	be	AUX
ejpam-6178	371	3	a	a	DET
ejpam-6178	371	4	map	map	NOUN
ejpam-6178	371	5	f	f	X
ejpam-6178	371	6	:	:	PUNCT
ejpam-6178	371	7	(	(	PUNCT
ejpam-6178	371	8	x	x	NOUN
ejpam-6178	371	9	,	,	PUNCT
ejpam-6178	371	10	◦	◦	NOUN
ejpam-6178	371	11	,	,	PUNCT
ejpam-6178	371	12	1x	1x	NUM
ejpam-6178	371	13	)	)	PUNCT
ejpam-6178	371	14	→	→	SYM
ejpam-6178	371	15	(	(	PUNCT
ejpam-6178	371	16	y	y	PROPN
ejpam-6178	371	17	,	,	PUNCT
ejpam-6178	371	18	∗	∗	NOUN
ejpam-6178	371	19	,	,	PUNCT
ejpam-6178	371	20	1y	1y	PROPN
ejpam-6178	371	21	)	)	PUNCT
ejpam-6178	371	22	is	be	AUX
ejpam-6178	371	23	a	a	DET
ejpam-6178	371	24	db	db	NOUN
ejpam-6178	371	25	-	-	PUNCT
ejpam-6178	371	26	isomorphism	isomorphism	NOUN
ejpam-6178	371	27	.	.	PUNCT
ejpam-6178	372	1	it	it	PRON
ejpam-6178	372	2	is	be	AUX
ejpam-6178	372	3	left	leave	VERB
ejpam-6178	372	4	to	to	PART
ejpam-6178	372	5	show	show	VERB
ejpam-6178	372	6	that	that	SCONJ
ejpam-6178	372	7	f	f	PROPN
ejpam-6178	372	8	is	be	AUX
ejpam-6178	372	9	continuous	continuous	ADJ
ejpam-6178	372	10	and	and	CCONJ
ejpam-6178	372	11	open	open	ADJ
ejpam-6178	372	12	.	.	PUNCT
ejpam-6178	373	1	let	let	VERB
ejpam-6178	373	2	u	u	PRON
ejpam-6178	373	3	be	be	AUX
ejpam-6178	373	4	open	open	ADJ
ejpam-6178	373	5	in	in	ADP
ejpam-6178	373	6	y	y	PROPN
ejpam-6178	373	7	and	and	CCONJ
ejpam-6178	373	8	[	[	X
ejpam-6178	373	9	x]s	x]s	PROPN
ejpam-6178	373	10	∈	∈	PROPN
ejpam-6178	373	11	f−1(u	f−1(u	PROPN
ejpam-6178	373	12	)	)	PUNCT
ejpam-6178	373	13	.	.	PUNCT
ejpam-6178	374	1	then	then	ADV
ejpam-6178	374	2	g(x	g(x	NOUN
ejpam-6178	374	3	)	)	PUNCT
ejpam-6178	374	4	=	=	SYM
ejpam-6178	374	5	f([x]s	f([x]s	X
ejpam-6178	374	6	)	)	PUNCT
ejpam-6178	374	7	∈	∈	PROPN
ejpam-6178	374	8	f(f−1(u	f(f−1(u	PROPN
ejpam-6178	374	9	)	)	PUNCT
ejpam-6178	374	10	)	)	PUNCT
ejpam-6178	375	1	⊆	⊆	X
ejpam-6178	375	2	u.	u.	NOUN
ejpam-6178	375	3	that	that	PRON
ejpam-6178	375	4	is	be	AUX
ejpam-6178	375	5	,	,	PUNCT
ejpam-6178	375	6	u	u	NOUN
ejpam-6178	375	7	is	be	AUX
ejpam-6178	375	8	a	a	DET
ejpam-6178	375	9	neighborhood	neighborhood	NOUN
ejpam-6178	375	10	of	of	ADP
ejpam-6178	375	11	g(x	g(x	NOUN
ejpam-6178	375	12	)	)	PUNCT
ejpam-6178	375	13	.	.	PUNCT
ejpam-6178	376	1	since	since	SCONJ
ejpam-6178	376	2	g	g	PROPN
ejpam-6178	376	3	is	be	AUX
ejpam-6178	376	4	continuous	continuous	ADJ
ejpam-6178	376	5	and	and	CCONJ
ejpam-6178	376	6	y	y	PROPN
ejpam-6178	376	7	∈	∈	PROPN
ejpam-6178	376	8	u	u	PROPN
ejpam-6178	376	9	,	,	PUNCT
ejpam-6178	376	10	it	it	PRON
ejpam-6178	376	11	follows	follow	VERB
ejpam-6178	376	12	from	from	ADP
ejpam-6178	376	13	theorem	theorem	NOUN
ejpam-6178	376	14	7	7	NUM
ejpam-6178	376	15	that	that	SCONJ
ejpam-6178	376	16	there	there	PRON
ejpam-6178	376	17	exists	exist	VERB
ejpam-6178	376	18	a	a	DET
ejpam-6178	376	19	neighborhood	neighborhood	NOUN
ejpam-6178	376	20	v	v	NOUN
ejpam-6178	376	21	of	of	ADP
ejpam-6178	376	22	x	x	PUNCT
ejpam-6178	376	23	such	such	ADJ
ejpam-6178	376	24	that	that	SCONJ
ejpam-6178	376	25	g(v	g(v	PROPN
ejpam-6178	376	26	)	)	PUNCT
ejpam-6178	376	27	⊆	⊆	NUM
ejpam-6178	376	28	u	u	NOUN
ejpam-6178	376	29	.	.	PUNCT
ejpam-6178	377	1	now	now	ADV
ejpam-6178	377	2	,	,	PUNCT
ejpam-6178	377	3	g	g	PROPN
ejpam-6178	377	4	is	be	AUX
ejpam-6178	377	5	continuous	continuous	ADJ
ejpam-6178	377	6	and	and	CCONJ
ejpam-6178	377	7	{	{	PUNCT
ejpam-6178	377	8	1y	1y	NOUN
ejpam-6178	377	9	}	}	PUNCT
ejpam-6178	377	10	is	be	AUX
ejpam-6178	377	11	open	open	ADJ
ejpam-6178	377	12	in	in	ADP
ejpam-6178	377	13	y	y	PROPN
ejpam-6178	377	14	,	,	PUNCT
ejpam-6178	377	15	it	it	PRON
ejpam-6178	377	16	follows	follow	VERB
ejpam-6178	377	17	that	that	PRON
ejpam-6178	377	18	s	s	VERB
ejpam-6178	378	1	=	=	ADJ
ejpam-6178	378	2	ker	ker	NOUN
ejpam-6178	378	3	g	g	PROPN
ejpam-6178	378	4	=	=	PROPN
ejpam-6178	378	5	g−1({1y	g−1({1y	PROPN
ejpam-6178	378	6	}	}	PUNCT
ejpam-6178	378	7	)	)	PUNCT
ejpam-6178	378	8	is	be	AUX
ejpam-6178	378	9	open	open	ADJ
ejpam-6178	378	10	in	in	ADP
ejpam-6178	378	11	x.	x.	NOUN
ejpam-6178	378	12	since	since	SCONJ
ejpam-6178	378	13	s	s	PROPN
ejpam-6178	378	14	is	be	AUX
ejpam-6178	378	15	open	open	ADJ
ejpam-6178	378	16	in	in	ADP
ejpam-6178	378	17	x	x	NOUN
ejpam-6178	378	18	,	,	PUNCT
ejpam-6178	378	19	then	then	ADV
ejpam-6178	378	20	by	by	ADP
ejpam-6178	378	21	theorem	theorem	NOUN
ejpam-6178	378	22	13	13	NUM
ejpam-6178	378	23	,	,	PUNCT
ejpam-6178	378	24	the	the	DET
ejpam-6178	378	25	natural	natural	ADJ
ejpam-6178	378	26	db	db	NOUN
ejpam-6178	378	27	-	-	PUNCT
ejpam-6178	378	28	homomorphism	homomorphism	NOUN
ejpam-6178	378	29	map	map	NOUN
ejpam-6178	378	30	φ	φ	PROPN
ejpam-6178	378	31	from	from	ADP
ejpam-6178	378	32	x	x	X
ejpam-6178	378	33	→	→	SYM
ejpam-6178	378	34	x	x	X
ejpam-6178	378	35	/	/	SYM
ejpam-6178	378	36	s	s	PART
ejpam-6178	378	37	is	be	AUX
ejpam-6178	378	38	an	an	DET
ejpam-6178	378	39	open	open	ADJ
ejpam-6178	378	40	mapping	mapping	NOUN
ejpam-6178	378	41	.	.	PUNCT
ejpam-6178	379	1	thus	thus	ADV
ejpam-6178	379	2	φ(v	φ(v	CCONJ
ejpam-6178	379	3	)	)	PUNCT
ejpam-6178	379	4	is	be	AUX
ejpam-6178	379	5	open	open	ADJ
ejpam-6178	379	6	in	in	ADP
ejpam-6178	379	7	x	x	X
ejpam-6178	379	8	/	/	SYM
ejpam-6178	379	9	s	s	PROPN
ejpam-6178	379	10	with	with	ADP
ejpam-6178	379	11	φ(x	φ(x	NOUN
ejpam-6178	379	12	)	)	PUNCT
ejpam-6178	379	13	=	=	PUNCT
ejpam-6178	380	1	[	[	X
ejpam-6178	380	2	x]s	x]s	PROPN
ejpam-6178	380	3	∈	∈	PROPN
ejpam-6178	380	4	φ(v	φ(v	ADV
ejpam-6178	380	5	)	)	PUNCT
ejpam-6178	380	6	.	.	PUNCT
ejpam-6178	381	1	now	now	ADV
ejpam-6178	381	2	,	,	PUNCT
ejpam-6178	381	3	f(φ(v	f(φ(v	PROPN
ejpam-6178	381	4	)	)	PUNCT
ejpam-6178	381	5	)	)	PUNCT
ejpam-6178	382	1	=	=	PRON
ejpam-6178	382	2	{	{	PUNCT
ejpam-6178	382	3	f([x′	f([x′	NOUN
ejpam-6178	382	4	]	]	PUNCT
ejpam-6178	382	5	)	)	PUNCT
ejpam-6178	383	1	|	|	ADV
ejpam-6178	384	1	[	[	X
ejpam-6178	384	2	x′	x′	X
ejpam-6178	384	3	]	]	X
ejpam-6178	384	4	∈	∈	PROPN
ejpam-6178	384	5	φ(v	φ(v	ADV
ejpam-6178	384	6	)	)	PUNCT
ejpam-6178	384	7	}	}	PUNCT
ejpam-6178	385	1	=	=	SYM
ejpam-6178	385	2	{	{	PUNCT
ejpam-6178	385	3	g(x′	g(x′	NOUN
ejpam-6178	385	4	)	)	PUNCT
ejpam-6178	386	1	|	|	ADV
ejpam-6178	386	2	x′	x′	PROPN
ejpam-6178	386	3	∈	∈	PROPN
ejpam-6178	386	4	v	v	ADP
ejpam-6178	386	5	}	}	PUNCT
ejpam-6178	386	6	=	=	SYM
ejpam-6178	386	7	g(v	g(v	X
ejpam-6178	386	8	)	)	PUNCT
ejpam-6178	387	1	⊆	⊆	NUM
ejpam-6178	387	2	u	u	NOUN
ejpam-6178	387	3	.	.	PUNCT
ejpam-6178	388	1	hence	hence	ADV
ejpam-6178	388	2	,	,	PUNCT
ejpam-6178	388	3	f−1(f(φ(v	f−1(f(φ(v	NOUN
ejpam-6178	388	4	)	)	PUNCT
ejpam-6178	388	5	)	)	PUNCT
ejpam-6178	389	1	⊆	⊆	NUM
ejpam-6178	389	2	f−1(u	f−1(u	NOUN
ejpam-6178	389	3	)	)	PUNCT
ejpam-6178	389	4	by	by	ADP
ejpam-6178	389	5	theorem	theorem	ADJ
ejpam-6178	389	6	9	9	NUM
ejpam-6178	389	7	(	(	PUNCT
ejpam-6178	389	8	iii	iii	NOUN
ejpam-6178	389	9	)	)	PUNCT
ejpam-6178	389	10	.	.	PUNCT
ejpam-6178	390	1	now	now	ADV
ejpam-6178	390	2	,	,	PUNCT
ejpam-6178	390	3	φ(v	φ(v	ADV
ejpam-6178	390	4	)	)	PUNCT
ejpam-6178	391	1	=	=	SYM
ejpam-6178	391	2	f−1(f(φ(v	f−1(f(φ(v	NOUN
ejpam-6178	391	3	)	)	PUNCT
ejpam-6178	391	4	)	)	PUNCT
ejpam-6178	392	1	⊆	⊆	NUM
ejpam-6178	392	2	f−1(u	f−1(u	NOUN
ejpam-6178	392	3	)	)	PUNCT
ejpam-6178	392	4	since	since	SCONJ
ejpam-6178	392	5	f	f	PROPN
ejpam-6178	392	6	is	be	AUX
ejpam-6178	392	7	one	one	NUM
ejpam-6178	392	8	-	-	PUNCT
ejpam-6178	392	9	to	to	ADP
ejpam-6178	392	10	-	-	PUNCT
ejpam-6178	392	11	one	one	NUM
ejpam-6178	392	12	.	.	PUNCT
ejpam-6178	393	1	therefore	therefore	ADV
ejpam-6178	393	2	,	,	PUNCT
ejpam-6178	393	3	for	for	ADP
ejpam-6178	393	4	every	every	DET
ejpam-6178	393	5	[	[	X
ejpam-6178	393	6	x]s	x]s	PROPN
ejpam-6178	393	7	∈	∈	PROPN
ejpam-6178	393	8	f−1(u	f−1(u	PROPN
ejpam-6178	393	9	)	)	PUNCT
ejpam-6178	393	10	,	,	PUNCT
ejpam-6178	393	11	there	there	PRON
ejpam-6178	393	12	exists	exist	VERB
ejpam-6178	393	13	a	a	DET
ejpam-6178	393	14	neighborhood	neighborhood	NOUN
ejpam-6178	393	15	φ(v	φ(v	ADV
ejpam-6178	393	16	)	)	PUNCT
ejpam-6178	393	17	of	of	ADP
ejpam-6178	393	18	[	[	X
ejpam-6178	393	19	x]s	x]s	NOUN
ejpam-6178	393	20	in	in	ADP
ejpam-6178	393	21	x	x	NOUN
ejpam-6178	393	22	/	/	SYM
ejpam-6178	393	23	s	s	VERB
ejpam-6178	393	24	such	such	ADJ
ejpam-6178	393	25	that	that	SCONJ
ejpam-6178	393	26	φ(v	φ(v	PROPN
ejpam-6178	393	27	)	)	PUNCT
ejpam-6178	393	28	⊆	⊆	NUM
ejpam-6178	393	29	f−1(u	f−1(u	NOUN
ejpam-6178	393	30	)	)	PUNCT
ejpam-6178	393	31	.	.	PUNCT
ejpam-6178	394	1	by	by	ADP
ejpam-6178	394	2	remark	remark	NOUN
ejpam-6178	394	3	2	2	NUM
ejpam-6178	394	4	,	,	PUNCT
ejpam-6178	394	5	f−1(u	f−1(u	PROPN
ejpam-6178	394	6	)	)	PUNCT
ejpam-6178	394	7	is	be	AUX
ejpam-6178	394	8	open	open	ADJ
ejpam-6178	394	9	in	in	ADP
ejpam-6178	394	10	x	x	X
ejpam-6178	394	11	/	/	SYM
ejpam-6178	394	12	s.	s.	PROPN
ejpam-6178	394	13	therefore	therefore	ADV
ejpam-6178	394	14	,	,	PUNCT
ejpam-6178	394	15	f	f	PROPN
ejpam-6178	394	16	is	be	AUX
ejpam-6178	394	17	continuous	continuous	ADJ
ejpam-6178	394	18	.	.	PUNCT
ejpam-6178	395	1	let	let	VERB
ejpam-6178	396	1	[	[	PUNCT
ejpam-6178	396	2	x]s	x]s	PROPN
ejpam-6178	396	3	∈	∈	PROPN
ejpam-6178	396	4	x	x	X
ejpam-6178	396	5	/	/	SYM
ejpam-6178	396	6	s	s	X
ejpam-6178	396	7	and	and	CCONJ
ejpam-6178	396	8	u	u	PRON
ejpam-6178	396	9	be	be	VERB
ejpam-6178	396	10	a	a	DET
ejpam-6178	396	11	neighborhood	neighborhood	NOUN
ejpam-6178	396	12	of	of	ADP
ejpam-6178	396	13	[	[	X
ejpam-6178	396	14	x]s	x]s	NOUN
ejpam-6178	396	15	in	in	ADP
ejpam-6178	396	16	x	x	PROPN
ejpam-6178	396	17	/	/	SYM
ejpam-6178	396	18	s.	s.	PROPN
ejpam-6178	396	19	then	then	ADV
ejpam-6178	396	20	f([x]s	f([x]s	PROPN
ejpam-6178	396	21	)	)	PUNCT
ejpam-6178	397	1	=	=	SYM
ejpam-6178	397	2	g(x	g(x	NOUN
ejpam-6178	397	3	)	)	PUNCT
ejpam-6178	397	4	∈	∈	PROPN
ejpam-6178	397	5	y	y	PROPN
ejpam-6178	397	6	.	.	PUNCT
ejpam-6178	398	1	since	since	SCONJ
ejpam-6178	398	2	φ(x	φ(x	NOUN
ejpam-6178	398	3	)	)	PUNCT
ejpam-6178	398	4	=	=	PUNCT
ejpam-6178	399	1	[	[	X
ejpam-6178	399	2	x]s	x]s	PROPN
ejpam-6178	399	3	∈	∈	PROPN
ejpam-6178	399	4	u	u	PROPN
ejpam-6178	399	5	,	,	PUNCT
ejpam-6178	399	6	then	then	ADV
ejpam-6178	399	7	x	x	SYM
ejpam-6178	399	8	∈	∈	PROPN
ejpam-6178	399	9	φ−1(u	φ−1(u	PROPN
ejpam-6178	399	10	)	)	PUNCT
ejpam-6178	399	11	.	.	PUNCT
ejpam-6178	400	1	since	since	SCONJ
ejpam-6178	400	2	the	the	DET
ejpam-6178	400	3	natural	natural	ADJ
ejpam-6178	400	4	db	db	NOUN
ejpam-6178	400	5	-	-	PUNCT
ejpam-6178	400	6	homomorphism	homomorphism	NOUN
ejpam-6178	400	7	φ	φ	PROPN
ejpam-6178	400	8	is	be	AUX
ejpam-6178	400	9	continuous	continuous	ADJ
ejpam-6178	400	10	,	,	PUNCT
ejpam-6178	400	11	φ−1(u	φ−1(u	PROPN
ejpam-6178	400	12	)	)	PUNCT
ejpam-6178	400	13	is	be	AUX
ejpam-6178	400	14	open	open	ADJ
ejpam-6178	400	15	in	in	ADP
ejpam-6178	400	16	x	x	PUNCT
ejpam-6178	400	17	which	which	PRON
ejpam-6178	400	18	contains	contain	VERB
ejpam-6178	400	19	x.	x.	NOUN
ejpam-6178	400	20	let	let	VERB
ejpam-6178	400	21	w	w	NOUN
ejpam-6178	400	22	=	=	SYM
ejpam-6178	400	23	φ−1(u	φ−1(u	PROPN
ejpam-6178	400	24	)	)	PUNCT
ejpam-6178	400	25	.	.	PUNCT
ejpam-6178	401	1	since	since	SCONJ
ejpam-6178	401	2	g	g	PROPN
ejpam-6178	401	3	is	be	AUX
ejpam-6178	401	4	an	an	DET
ejpam-6178	401	5	open	open	ADJ
ejpam-6178	401	6	mapping	mapping	NOUN
ejpam-6178	401	7	,	,	PUNCT
ejpam-6178	401	8	g(w	g(w	PROPN
ejpam-6178	401	9	)	)	PUNCT
ejpam-6178	401	10	is	be	AUX
ejpam-6178	401	11	open	open	ADJ
ejpam-6178	401	12	in	in	ADP
ejpam-6178	401	13	y	y	PROPN
ejpam-6178	401	14	and	and	CCONJ
ejpam-6178	401	15	f([x]s	f([x]s	ADJ
ejpam-6178	401	16	)	)	PUNCT
ejpam-6178	401	17	=	=	SYM
ejpam-6178	401	18	g(x	g(x	NOUN
ejpam-6178	401	19	)	)	PUNCT
ejpam-6178	401	20	∈	∈	PROPN
ejpam-6178	401	21	g(w	g(w	PROPN
ejpam-6178	401	22	)	)	PUNCT
ejpam-6178	401	23	.	.	PUNCT
ejpam-6178	402	1	by	by	ADP
ejpam-6178	402	2	remark	remark	NOUN
ejpam-6178	402	3	2	2	NUM
ejpam-6178	402	4	,	,	PUNCT
ejpam-6178	402	5	there	there	PRON
ejpam-6178	402	6	exists	exist	VERB
ejpam-6178	402	7	a	a	DET
ejpam-6178	402	8	neighborhood	neighborhood	NOUN
ejpam-6178	402	9	g	g	NOUN
ejpam-6178	402	10	of	of	ADP
ejpam-6178	402	11	f([x]s	f([x]s	NOUN
ejpam-6178	402	12	)	)	PUNCT
ejpam-6178	402	13	in	in	ADP
ejpam-6178	402	14	y	y	PROPN
ejpam-6178	402	15	with	with	ADP
ejpam-6178	402	16	g	g	PROPN
ejpam-6178	402	17	⊆	⊆	NUM
ejpam-6178	402	18	g(w	g(w	PROPN
ejpam-6178	402	19	)	)	PUNCT
ejpam-6178	402	20	.	.	PUNCT
ejpam-6178	403	1	let	let	VERB
ejpam-6178	403	2	a	a	DET
ejpam-6178	403	3	∈	∈	PROPN
ejpam-6178	403	4	f−1(g	f−1(g	NOUN
ejpam-6178	403	5	)	)	PUNCT
ejpam-6178	403	6	.	.	PUNCT
ejpam-6178	404	1	then	then	ADV
ejpam-6178	404	2	f(a	f(a	X
ejpam-6178	404	3	)	)	PUNCT
ejpam-6178	404	4	∈	∈	PROPN
ejpam-6178	404	5	g	g	ADP
ejpam-6178	404	6	⊆	⊆	NUM
ejpam-6178	404	7	g(w	g(w	PROPN
ejpam-6178	404	8	)	)	PUNCT
ejpam-6178	404	9	.	.	PUNCT
ejpam-6178	405	1	that	that	PRON
ejpam-6178	405	2	is	be	AUX
ejpam-6178	405	3	,	,	PUNCT
ejpam-6178	405	4	f(a	f(a	NOUN
ejpam-6178	405	5	)	)	PUNCT
ejpam-6178	405	6	=	=	SYM
ejpam-6178	405	7	g(a′	g(a′	NOUN
ejpam-6178	405	8	)	)	PUNCT
ejpam-6178	405	9	for	for	ADP
ejpam-6178	405	10	some	some	DET
ejpam-6178	405	11	a′	a′	NOUN
ejpam-6178	405	12	∈	∈	PROPN
ejpam-6178	405	13	w	w	PROPN
ejpam-6178	405	14	.	.	PUNCT
ejpam-6178	406	1	since	since	SCONJ
ejpam-6178	406	2	a′	a′	PROPN
ejpam-6178	406	3	∈	∈	PROPN
ejpam-6178	406	4	w	w	PROPN
ejpam-6178	406	5	=	=	SYM
ejpam-6178	406	6	φ−1(u	φ−1(u	PROPN
ejpam-6178	406	7	)	)	PUNCT
ejpam-6178	406	8	,	,	PUNCT
ejpam-6178	406	9	[	[	X
ejpam-6178	406	10	a′]s	a′]s	ADP
ejpam-6178	406	11	=	=	PUNCT
ejpam-6178	406	12	φ(a′	φ(a′	PROPN
ejpam-6178	406	13	)	)	PUNCT
ejpam-6178	406	14	∈	∈	PROPN
ejpam-6178	406	15	u	u	NOUN
ejpam-6178	406	16	.	.	PUNCT
ejpam-6178	407	1	thus	thus	ADV
ejpam-6178	407	2	,	,	PUNCT
ejpam-6178	407	3	a	a	DET
ejpam-6178	407	4	=	=	SYM
ejpam-6178	407	5	f−1(f(a	f−1(f(a	NOUN
ejpam-6178	407	6	)	)	PUNCT
ejpam-6178	407	7	)	)	PUNCT
ejpam-6178	408	1	=	=	PUNCT
ejpam-6178	408	2	f−1(g(a′	f−1(g(a′	NOUN
ejpam-6178	408	3	)	)	PUNCT
ejpam-6178	408	4	)	)	PUNCT
ejpam-6178	409	1	=	=	SYM
ejpam-6178	409	2	f−1(f([a′]s	f−1(f([a′]s	NOUN
ejpam-6178	409	3	)	)	PUNCT
ejpam-6178	409	4	)	)	PUNCT
ejpam-6178	410	1	=	=	PUNCT
ejpam-6178	411	1	[	[	X
ejpam-6178	411	2	a′]s	a′]s	ADP
ejpam-6178	411	3	∈	∈	PROPN
ejpam-6178	411	4	u	u	NOUN
ejpam-6178	411	5	which	which	PRON
ejpam-6178	411	6	implies	imply	VERB
ejpam-6178	411	7	that	that	PRON
ejpam-6178	411	8	f−1(g	f−1(g	PROPN
ejpam-6178	411	9	)	)	PUNCT
ejpam-6178	411	10	⊆	⊆	NUM
ejpam-6178	411	11	u	u	NOUN
ejpam-6178	411	12	.	.	PUNCT
ejpam-6178	412	1	hence	hence	ADV
ejpam-6178	412	2	,	,	PUNCT
ejpam-6178	412	3	g	g	PROPN
ejpam-6178	412	4	=	=	PROPN
ejpam-6178	412	5	f(f−1(g	f(f−1(g	PROPN
ejpam-6178	412	6	)	)	PUNCT
ejpam-6178	412	7	)	)	PUNCT
ejpam-6178	413	1	⊆	⊆	NUM
ejpam-6178	413	2	f(u	f(u	PROPN
ejpam-6178	413	3	)	)	PUNCT
ejpam-6178	413	4	since	since	SCONJ
ejpam-6178	413	5	f	f	PROPN
ejpam-6178	413	6	is	be	AUX
ejpam-6178	413	7	surjective	surjective	ADJ
ejpam-6178	413	8	.	.	PUNCT
ejpam-6178	414	1	by	by	ADP
ejpam-6178	414	2	theorem	theorem	NOUN
ejpam-6178	414	3	6	6	NUM
ejpam-6178	414	4	,	,	PUNCT
ejpam-6178	414	5	f	f	PROPN
ejpam-6178	414	6	is	be	AUX
ejpam-6178	414	7	open	open	ADJ
ejpam-6178	414	8	.	.	PUNCT
ejpam-6178	415	1	consequently	consequently	ADV
ejpam-6178	415	2	,	,	PUNCT
ejpam-6178	415	3	f	f	PROPN
ejpam-6178	415	4	is	be	AUX
ejpam-6178	415	5	a	a	DET
ejpam-6178	415	6	tdb	tdb	PROPN
ejpam-6178	415	7	-	-	PUNCT
ejpam-6178	415	8	isomorphism	isomorphism	NOUN
ejpam-6178	415	9	.	.	PUNCT
ejpam-6178	416	1	the	the	DET
ejpam-6178	416	2	next	next	ADJ
ejpam-6178	416	3	result	result	NOUN
ejpam-6178	416	4	is	be	AUX
ejpam-6178	416	5	a	a	DET
ejpam-6178	416	6	consequence	consequence	NOUN
ejpam-6178	416	7	of	of	ADP
ejpam-6178	416	8	theorem	theorem	NOUN
ejpam-6178	416	9	17	17	NUM
ejpam-6178	416	10	.	.	PUNCT
ejpam-6178	417	1	with	with	ADP
ejpam-6178	417	2	ker	ker	PROPN
ejpam-6178	417	3	g	g	PROPN
ejpam-6178	417	4	=	=	PUNCT
ejpam-6178	417	5	{	{	PUNCT
ejpam-6178	417	6	1x	1x	NUM
ejpam-6178	417	7	}	}	PUNCT
ejpam-6178	417	8	,	,	PUNCT
ejpam-6178	417	9	g	g	PROPN
ejpam-6178	417	10	is	be	AUX
ejpam-6178	417	11	one	one	NUM
ejpam-6178	417	12	-	-	PUNCT
ejpam-6178	417	13	to	to	ADP
ejpam-6178	417	14	-	-	PUNCT
ejpam-6178	417	15	one	one	NUM
ejpam-6178	417	16	by	by	ADP
ejpam-6178	417	17	theorem	theorem	NOUN
ejpam-6178	417	18	3	3	NUM
ejpam-6178	417	19	and	and	CCONJ
ejpam-6178	417	20	by	by	ADP
ejpam-6178	417	21	theorem	theorem	NOUN
ejpam-6178	417	22	17	17	NUM
ejpam-6178	417	23	,	,	PUNCT
ejpam-6178	417	24	g	g	PROPN
ejpam-6178	417	25	is	be	AUX
ejpam-6178	417	26	open	open	ADJ
ejpam-6178	417	27	,	,	PUNCT
ejpam-6178	417	28	continuous	continuous	ADJ
ejpam-6178	417	29	,	,	PUNCT
ejpam-6178	417	30	and	and	CCONJ
ejpam-6178	417	31	surjective	surjective	ADJ
ejpam-6178	417	32	.	.	PUNCT
ejpam-6178	418	1	by	by	ADP
ejpam-6178	418	2	definition	definition	NOUN
ejpam-6178	418	3	15	15	NUM
ejpam-6178	418	4	,	,	PUNCT
ejpam-6178	418	5	g	g	PROPN
ejpam-6178	418	6	is	be	AUX
ejpam-6178	418	7	a	a	DET
ejpam-6178	418	8	tdb	tdb	PROPN
ejpam-6178	418	9	-	-	PUNCT
ejpam-6178	418	10	isomorphism	isomorphism	NOUN
ejpam-6178	418	11	.	.	PUNCT
ejpam-6178	419	1	corollary	corollary	ADJ
ejpam-6178	419	2	6	6	NUM
ejpam-6178	419	3	.	.	PUNCT
ejpam-6178	420	1	let	let	VERB
ejpam-6178	420	2	(	(	PUNCT
ejpam-6178	420	3	x	x	NOUN
ejpam-6178	420	4	,	,	PUNCT
ejpam-6178	420	5	◦	◦	NOUN
ejpam-6178	420	6	,	,	PUNCT
ejpam-6178	420	7	τ	τ	PROPN
ejpam-6178	420	8	and	and	CCONJ
ejpam-6178	420	9	(	(	PUNCT
ejpam-6178	420	10	y	y	PROPN
ejpam-6178	420	11	,	,	PUNCT
ejpam-6178	420	12	∗	∗	NOUN
ejpam-6178	420	13	,	,	PUNCT
ejpam-6178	420	14	τ	τ	PROPN
ejpam-6178	420	15	′	′	NUM
ejpam-6178	420	16	)	)	PUNCT
ejpam-6178	420	17	be	be	AUX
ejpam-6178	420	18	tdb	tdb	PROPN
ejpam-6178	420	19	-	-	PUNCT
ejpam-6178	420	20	algebras	algebras	PROPN
ejpam-6178	420	21	with	with	ADP
ejpam-6178	420	22	{	{	PUNCT
ejpam-6178	420	23	1y	1y	NOUN
ejpam-6178	420	24	}	}	PUNCT
ejpam-6178	420	25	open	open	ADJ
ejpam-6178	420	26	in	in	ADP
ejpam-6178	420	27	y	y	PROPN
ejpam-6178	420	28	.	.	PUNCT
ejpam-6178	421	1	if	if	SCONJ
ejpam-6178	421	2	g	g	PROPN
ejpam-6178	421	3	is	be	AUX
ejpam-6178	421	4	an	an	DET
ejpam-6178	421	5	open	open	ADJ
ejpam-6178	421	6	tdb	tdb	NOUN
ejpam-6178	421	7	-	-	NOUN
ejpam-6178	421	8	homomorphism	homomorphism	NOUN
ejpam-6178	421	9	from	from	ADP
ejpam-6178	421	10	(	(	PUNCT
ejpam-6178	421	11	x	x	NOUN
ejpam-6178	421	12	,	,	PUNCT
ejpam-6178	421	13	◦	◦	NOUN
ejpam-6178	421	14	,	,	PUNCT
ejpam-6178	421	15	τ	τ	X
ejpam-6178	421	16	)	)	PUNCT
ejpam-6178	421	17	onto	onto	ADP
ejpam-6178	421	18	(	(	PUNCT
ejpam-6178	421	19	y	y	PROPN
ejpam-6178	421	20	,	,	PUNCT
ejpam-6178	421	21	∗	∗	NOUN
ejpam-6178	421	22	,	,	PUNCT
ejpam-6178	421	23	τ	τ	PROPN
ejpam-6178	421	24	′	′	NOUN
ejpam-6178	421	25	)	)	PUNCT
ejpam-6178	421	26	having	have	VERB
ejpam-6178	421	27	kerg	kerg	PROPN
ejpam-6178	421	28	=	=	PUNCT
ejpam-6178	421	29	{	{	PUNCT
ejpam-6178	421	30	1x	1x	NUM
ejpam-6178	421	31	}	}	PUNCT
ejpam-6178	421	32	,	,	PUNCT
ejpam-6178	421	33	then	then	ADV
ejpam-6178	421	34	g	g	PROPN
ejpam-6178	421	35	is	be	AUX
ejpam-6178	421	36	a	a	DET
ejpam-6178	421	37	tdb	tdb	PROPN
ejpam-6178	421	38	-	-	PUNCT
ejpam-6178	421	39	isomorphism	isomorphism	NOUN
ejpam-6178	421	40	.	.	PUNCT
ejpam-6178	422	1	that	that	PRON
ejpam-6178	422	2	is	be	AUX
ejpam-6178	422	3	,	,	PUNCT
ejpam-6178	422	4	x	x	X
ejpam-6178	422	5	is	be	AUX
ejpam-6178	422	6	topologically	topologically	ADV
ejpam-6178	422	7	isomorphic	isomorphic	ADJ
ejpam-6178	422	8	to	to	ADP
ejpam-6178	422	9	y	y	PROPN
ejpam-6178	422	10	.	.	PUNCT
ejpam-6178	423	1	4	4	X
ejpam-6178	423	2	.	.	X
ejpam-6178	423	3	conclusions	conclusion	NOUN
ejpam-6178	423	4	this	this	DET
ejpam-6178	423	5	study	study	NOUN
ejpam-6178	423	6	provided	provide	VERB
ejpam-6178	423	7	the	the	DET
ejpam-6178	423	8	existence	existence	NOUN
ejpam-6178	423	9	of	of	ADP
ejpam-6178	423	10	the	the	DET
ejpam-6178	423	11	tdb	tdb	PROPN
ejpam-6178	423	12	-	-	NOUN
ejpam-6178	423	13	homomorphism	homomorphism	NOUN
ejpam-6178	423	14	with	with	ADP
ejpam-6178	423	15	the	the	DET
ejpam-6178	423	16	use	use	NOUN
ejpam-6178	423	17	of	of	ADP
ejpam-6178	423	18	a	a	DET
ejpam-6178	423	19	program	program	NOUN
ejpam-6178	423	20	and	and	CCONJ
ejpam-6178	423	21	manual	manual	ADJ
ejpam-6178	423	22	computations	computation	NOUN
ejpam-6178	423	23	.	.	PUNCT
ejpam-6178	424	1	moreover	moreover	ADV
ejpam-6178	424	2	,	,	PUNCT
ejpam-6178	424	3	this	this	DET
ejpam-6178	424	4	study	study	NOUN
ejpam-6178	424	5	proved	prove	VERB
ejpam-6178	424	6	that	that	SCONJ
ejpam-6178	424	7	it	it	PRON
ejpam-6178	424	8	is	be	AUX
ejpam-6178	424	9	possible	possible	ADJ
ejpam-6178	424	10	to	to	PART
ejpam-6178	424	11	construct	construct	VERB
ejpam-6178	424	12	a	a	DET
ejpam-6178	424	13	topology	topology	NOUN
ejpam-6178	424	14	for	for	ADP
ejpam-6178	424	15	the	the	DET
ejpam-6178	424	16	quotient	quotient	NOUN
ejpam-6178	424	17	dual	dual	ADJ
ejpam-6178	424	18	b	b	X
ejpam-6178	424	19	-	-	PUNCT
ejpam-6178	424	20	algebra	algebra	NOUN
ejpam-6178	424	21	using	use	VERB
ejpam-6178	424	22	the	the	DET
ejpam-6178	424	23	natural	natural	ADJ
ejpam-6178	424	24	db	db	NOUN
ejpam-6178	424	25	-	-	PUNCT
ejpam-6178	424	26	homomorphism	homomorphism	NOUN
ejpam-6178	424	27	in	in	ADP
ejpam-6178	424	28	such	such	DET
ejpam-6178	424	29	a	a	DET
ejpam-6178	424	30	way	way	NOUN
ejpam-6178	424	31	that	that	PRON
ejpam-6178	424	32	it	it	PRON
ejpam-6178	424	33	will	will	AUX
ejpam-6178	424	34	be	be	AUX
ejpam-6178	424	35	useful	useful	ADJ
ejpam-6178	424	36	in	in	ADP
ejpam-6178	424	37	establishing	establish	VERB
ejpam-6178	424	38	the	the	DET
ejpam-6178	424	39	tdb	tdb	PROPN
ejpam-6178	424	40	-	-	NOUN
ejpam-6178	424	41	homomorphism	homomorphism	PROPN
ejpam-6178	424	42	and	and	CCONJ
ejpam-6178	424	43	the	the	DET
ejpam-6178	424	44	tdb	tdb	PROPN
ejpam-6178	424	45	-	-	PUNCT
ejpam-6178	424	46	isomorphism	isomorphism	NOUN
ejpam-6178	424	47	.	.	PUNCT
ejpam-6178	425	1	indeed	indeed	ADV
ejpam-6178	425	2	,	,	PUNCT
ejpam-6178	425	3	most	most	ADJ
ejpam-6178	425	4	of	of	ADP
ejpam-6178	425	5	the	the	DET
ejpam-6178	425	6	results	result	NOUN
ejpam-6178	425	7	were	be	AUX
ejpam-6178	425	8	anchored	anchor	VERB
ejpam-6178	425	9	on	on	ADP
ejpam-6178	425	10	this	this	DET
ejpam-6178	425	11	topology	topology	NOUN
ejpam-6178	425	12	.	.	PUNCT
ejpam-6178	426	1	this	this	DET
ejpam-6178	426	2	study	study	NOUN
ejpam-6178	426	3	also	also	ADV
ejpam-6178	426	4	introduced	introduce	VERB
ejpam-6178	426	5	the	the	DET
ejpam-6178	426	6	r.	r.	PROPN
ejpam-6178	426	7	nuñez	nuñez	PROPN
ejpam-6178	426	8	,	,	PUNCT
ejpam-6178	426	9	k.	k.	PROPN
ejpam-6178	426	10	b.	b.	PROPN
ejpam-6178	426	11	fuentes	fuentes	PROPN
ejpam-6178	426	12	/	/	SYM
ejpam-6178	426	13	eur	eur	PROPN
ejpam-6178	426	14	.	.	PUNCT
ejpam-6178	427	1	j.	j.	PROPN
ejpam-6178	427	2	pure	pure	PROPN
ejpam-6178	427	3	appl	appl	PROPN
ejpam-6178	427	4	.	.	PROPN
ejpam-6178	427	5	math	math	PROPN
ejpam-6178	427	6	,	,	PUNCT
ejpam-6178	427	7	18	18	NUM
ejpam-6178	427	8	(	(	PUNCT
ejpam-6178	427	9	4	4	NUM
ejpam-6178	427	10	)	)	PUNCT
ejpam-6178	427	11	(	(	PUNCT
ejpam-6178	427	12	2025	2025	NUM
ejpam-6178	427	13	)	)	PUNCT
ejpam-6178	427	14	,	,	PUNCT
ejpam-6178	427	15	6178	6178	NUM
ejpam-6178	427	16	12	12	NUM
ejpam-6178	427	17	of	of	ADP
ejpam-6178	427	18	15	15	NUM
ejpam-6178	427	19	transitive	transitive	ADJ
ejpam-6178	427	20	tdb	tdb	NOUN
ejpam-6178	427	21	-	-	PUNCT
ejpam-6178	427	22	algebras	algebras	PROPN
ejpam-6178	427	23	and	and	CCONJ
ejpam-6178	427	24	some	some	PRON
ejpam-6178	427	25	of	of	ADP
ejpam-6178	427	26	its	its	PRON
ejpam-6178	427	27	properties	property	NOUN
ejpam-6178	427	28	.	.	PUNCT
ejpam-6178	428	1	these	these	DET
ejpam-6178	428	2	properties	property	NOUN
ejpam-6178	428	3	were	be	AUX
ejpam-6178	428	4	used	use	VERB
ejpam-6178	428	5	to	to	PART
ejpam-6178	428	6	obtain	obtain	VERB
ejpam-6178	428	7	a	a	DET
ejpam-6178	428	8	tdb	tdb	NOUN
ejpam-6178	428	9	-	-	NOUN
ejpam-6178	428	10	homomorphism	homomorphism	NOUN
ejpam-6178	428	11	between	between	ADP
ejpam-6178	428	12	transitive	transitive	ADJ
ejpam-6178	428	13	open	open	ADJ
ejpam-6178	428	14	tdb	tdb	NOUN
ejpam-6178	428	15	-	-	PUNCT
ejpam-6178	428	16	algebras	algebra	NOUN
ejpam-6178	428	17	.	.	PUNCT
ejpam-6178	429	1	future	future	ADJ
ejpam-6178	429	2	works	work	NOUN
ejpam-6178	429	3	may	may	AUX
ejpam-6178	429	4	explore	explore	VERB
ejpam-6178	429	5	characterization	characterization	NOUN
ejpam-6178	429	6	theorems	theorem	NOUN
ejpam-6178	429	7	for	for	ADP
ejpam-6178	429	8	the	the	DET
ejpam-6178	429	9	topological	topological	ADJ
ejpam-6178	429	10	dual	dual	PROPN
ejpam-6178	429	11	b	b	NOUN
ejpam-6178	429	12	-	-	PUNCT
ejpam-6178	429	13	homomorphisms	homomorphism	NOUN
ejpam-6178	429	14	.	.	PUNCT
ejpam-6178	430	1	that	that	PRON
ejpam-6178	430	2	is	is	ADV
ejpam-6178	430	3	,	,	PUNCT
ejpam-6178	430	4	given	give	VERB
ejpam-6178	430	5	an	an	DET
ejpam-6178	430	6	arbitrary	arbitrary	ADJ
ejpam-6178	430	7	mapping	mapping	NOUN
ejpam-6178	430	8	between	between	ADP
ejpam-6178	430	9	topological	topological	ADJ
ejpam-6178	430	10	dual	dual	PROPN
ejpam-6178	430	11	b	b	NOUN
ejpam-6178	430	12	-	-	PUNCT
ejpam-6178	430	13	algebras	algebras	PROPN
ejpam-6178	430	14	provide	provide	VERB
ejpam-6178	430	15	a	a	DET
ejpam-6178	430	16	necessary	necessary	ADJ
ejpam-6178	430	17	and	and	CCONJ
ejpam-6178	430	18	sufficient	sufficient	ADJ
ejpam-6178	430	19	condition	condition	NOUN
ejpam-6178	430	20	to	to	PART
ejpam-6178	430	21	conclude	conclude	VERB
ejpam-6178	430	22	that	that	SCONJ
ejpam-6178	430	23	the	the	DET
ejpam-6178	430	24	map	map	NOUN
ejpam-6178	430	25	is	be	AUX
ejpam-6178	430	26	a	a	DET
ejpam-6178	430	27	topological	topological	ADJ
ejpam-6178	430	28	dual	dual	ADJ
ejpam-6178	430	29	b	b	NOUN
ejpam-6178	430	30	-	-	PUNCT
ejpam-6178	430	31	homomorphism	homomorphism	NOUN
ejpam-6178	430	32	.	.	PUNCT
ejpam-6178	431	1	acknowledgements	acknowledgement	NOUN
ejpam-6178	431	2	the	the	DET
ejpam-6178	431	3	authors	author	NOUN
ejpam-6178	431	4	are	be	AUX
ejpam-6178	431	5	grateful	grateful	ADJ
ejpam-6178	431	6	to	to	ADP
ejpam-6178	431	7	the	the	DET
ejpam-6178	431	8	department	department	NOUN
ejpam-6178	431	9	of	of	ADP
ejpam-6178	431	10	science	science	NOUN
ejpam-6178	431	11	and	and	CCONJ
ejpam-6178	431	12	technology	technology	NOUN
ejpam-6178	431	13	(	(	PUNCT
ejpam-6178	431	14	dost	dost	NOUN
ejpam-6178	431	15	)	)	PUNCT
ejpam-6178	431	16	through	through	ADP
ejpam-6178	431	17	the	the	DET
ejpam-6178	431	18	accelerated	accelerated	ADJ
ejpam-6178	431	19	science	science	NOUN
ejpam-6178	431	20	and	and	CCONJ
ejpam-6178	431	21	technology	technology	NOUN
ejpam-6178	431	22	human	human	ADJ
ejpam-6178	431	23	resource	resource	NOUN
ejpam-6178	431	24	development	development	NOUN
ejpam-6178	431	25	program	program	NOUN
ejpam-6178	431	26	(	(	PUNCT
ejpam-6178	431	27	asthrdp	asthrdp	PROPN
ejpam-6178	431	28	)	)	PUNCT
ejpam-6178	431	29	and	and	CCONJ
ejpam-6178	431	30	its	its	PRON
ejpam-6178	431	31	partner	partner	NOUN
ejpam-6178	431	32	university	university	NOUN
ejpam-6178	431	33	,	,	PUNCT
ejpam-6178	431	34	university	university	PROPN
ejpam-6178	431	35	of	of	ADP
ejpam-6178	431	36	san	san	PROPN
ejpam-6178	431	37	carlos	carlos	PROPN
ejpam-6178	431	38	who	who	PRON
ejpam-6178	431	39	funded	fund	VERB
ejpam-6178	431	40	and	and	CCONJ
ejpam-6178	431	41	made	make	VERB
ejpam-6178	431	42	this	this	DET
ejpam-6178	431	43	research	research	NOUN
ejpam-6178	431	44	possible	possible	ADJ
ejpam-6178	431	45	.	.	PUNCT
ejpam-6178	432	1	references	reference	NOUN
ejpam-6178	432	2	[	[	X
ejpam-6178	432	3	1	1	NUM
ejpam-6178	432	4	]	]	PUNCT
ejpam-6178	432	5	k.	k.	PROPN
ejpam-6178	432	6	iseki	iseki	PROPN
ejpam-6178	432	7	.	.	PUNCT
ejpam-6178	433	1	an	an	DET
ejpam-6178	433	2	algebra	algebra	NOUN
ejpam-6178	433	3	related	relate	VERB
ejpam-6178	433	4	with	with	ADP
ejpam-6178	433	5	a	a	DET
ejpam-6178	433	6	propositional	propositional	ADJ
ejpam-6178	433	7	calculus	calculus	NOUN
ejpam-6178	433	8	.	.	PUNCT
ejpam-6178	434	1	proceedings	proceeding	NOUN
ejpam-6178	434	2	of	of	ADP
ejpam-6178	434	3	the	the	DET
ejpam-6178	434	4	japan	japan	PROPN
ejpam-6178	434	5	academy	academy	PROPN
ejpam-6178	434	6	,	,	PUNCT
ejpam-6178	434	7	42(1):26–29	42(1):26–29	NUM
ejpam-6178	434	8	,	,	PUNCT
ejpam-6178	434	9	1966	1966	NUM
ejpam-6178	434	10	.	.	PUNCT
ejpam-6178	435	1	[	[	X
ejpam-6178	435	2	2	2	NUM
ejpam-6178	435	3	]	]	X
ejpam-6178	435	4	yasuyuki	yasuyuki	PROPN
ejpam-6178	435	5	imai	imai	PROPN
ejpam-6178	435	6	and	and	CCONJ
ejpam-6178	435	7	kiyoshi	kiyoshi	PROPN
ejpam-6178	435	8	iséki	iséki	PROPN
ejpam-6178	435	9	.	.	PROPN
ejpam-6178	436	1	on	on	ADP
ejpam-6178	436	2	axiom	axiom	NOUN
ejpam-6178	436	3	systems	system	NOUN
ejpam-6178	436	4	of	of	ADP
ejpam-6178	436	5	propositional	propositional	ADJ
ejpam-6178	436	6	calculi	calculi	PROPN
ejpam-6178	436	7	,	,	PUNCT
ejpam-6178	436	8	xiv	xiv	PROPN
ejpam-6178	436	9	.	.	PUNCT
ejpam-6178	437	1	proceedings	proceeding	NOUN
ejpam-6178	437	2	of	of	ADP
ejpam-6178	437	3	the	the	DET
ejpam-6178	437	4	japan	japan	PROPN
ejpam-6178	437	5	academy	academy	PROPN
ejpam-6178	437	6	,	,	PUNCT
ejpam-6178	437	7	42(1):19	42(1):19	PROPN
ejpam-6178	437	8	–	–	PUNCT
ejpam-6178	437	9	22	22	NUM
ejpam-6178	437	10	,	,	PUNCT
ejpam-6178	437	11	1966	1966	NUM
ejpam-6178	437	12	.	.	PUNCT
ejpam-6178	438	1	[	[	X
ejpam-6178	438	2	3	3	X
ejpam-6178	438	3	]	]	PUNCT
ejpam-6178	438	4	qingping	qingpe	VERB
ejpam-6178	438	5	hu	hu	PROPN
ejpam-6178	438	6	and	and	CCONJ
ejpam-6178	438	7	xin	xin	PROPN
ejpam-6178	438	8	li	li	PROPN
ejpam-6178	438	9	.	.	PROPN
ejpam-6178	439	1	on	on	ADP
ejpam-6178	439	2	bch	bch	PROPN
ejpam-6178	439	3	-	-	PUNCT
ejpam-6178	439	4	algebras	algebras	PROPN
ejpam-6178	439	5	.	.	PUNCT
ejpam-6178	439	6	math	math	PROPN
ejpam-6178	439	7	.	.	PUNCT
ejpam-6178	440	1	semin	semin	PROPN
ejpam-6178	440	2	.	.	PUNCT
ejpam-6178	441	1	notes	notes	PROPN
ejpam-6178	441	2	,	,	PUNCT
ejpam-6178	441	3	kobe	kobe	PROPN
ejpam-6178	441	4	univ	univ	PROPN
ejpam-6178	441	5	.	.	PROPN
ejpam-6178	441	6	,	,	PUNCT
ejpam-6178	441	7	11:313–320	11:313–320	PROPN
ejpam-6178	441	8	,	,	PUNCT
ejpam-6178	441	9	1983	1983	NUM
ejpam-6178	441	10	.	.	PUNCT
ejpam-6178	442	1	[	[	X
ejpam-6178	442	2	4	4	X
ejpam-6178	442	3	]	]	X
ejpam-6178	442	4	a	a	DET
ejpam-6178	442	5	iampan	iampan	NOUN
ejpam-6178	442	6	.	.	PUNCT
ejpam-6178	443	1	a	a	DET
ejpam-6178	443	2	new	new	ADJ
ejpam-6178	443	3	branch	branch	NOUN
ejpam-6178	443	4	of	of	ADP
ejpam-6178	443	5	the	the	DET
ejpam-6178	443	6	logical	logical	ADJ
ejpam-6178	443	7	algebra	algebra	NOUN
ejpam-6178	443	8	:	:	PUNCT
ejpam-6178	443	9	up	up	ADP
ejpam-6178	443	10	-	-	PUNCT
ejpam-6178	443	11	algebras	algebras	X
ejpam-6178	443	12	.	.	PUNCT
ejpam-6178	443	13	journal	journal	PROPN
ejpam-6178	443	14	of	of	ADP
ejpam-6178	443	15	algebra	algebra	PROPN
ejpam-6178	443	16	and	and	CCONJ
ejpam-6178	443	17	related	related	ADJ
ejpam-6178	443	18	topics	topic	NOUN
ejpam-6178	443	19	,	,	PUNCT
ejpam-6178	443	20	5(1):35–54	5(1):35–54	NUM
ejpam-6178	443	21	,	,	PUNCT
ejpam-6178	443	22	2017	2017	NUM
ejpam-6178	443	23	.	.	PUNCT
ejpam-6178	444	1	[	[	X
ejpam-6178	444	2	5	5	X
ejpam-6178	444	3	]	]	PUNCT
ejpam-6178	444	4	j.	j.	PROPN
ejpam-6178	444	5	neggers	neggers	PROPN
ejpam-6178	444	6	and	and	CCONJ
ejpam-6178	444	7	hee	hee	PROPN
ejpam-6178	444	8	sik	sik	PROPN
ejpam-6178	444	9	kim	kim	PROPN
ejpam-6178	444	10	.	.	PUNCT
ejpam-6178	445	1	on	on	ADP
ejpam-6178	445	2	b	b	NOUN
ejpam-6178	445	3	-	-	PUNCT
ejpam-6178	445	4	algebras	algebras	PROPN
ejpam-6178	445	5	.	.	PUNCT
ejpam-6178	446	1	international	international	ADJ
ejpam-6178	446	2	mathematical	mathematical	ADJ
ejpam-6178	446	3	journal	journal	NOUN
ejpam-6178	446	4	,	,	PUNCT
ejpam-6178	446	5	2	2	NUM
ejpam-6178	446	6	,	,	PUNCT
ejpam-6178	446	7	01	01	NUM
ejpam-6178	446	8	2002	2002	NUM
ejpam-6178	446	9	.	.	PUNCT
ejpam-6178	447	1	[	[	X
ejpam-6178	447	2	6	6	NUM
ejpam-6178	447	3	]	]	PUNCT
ejpam-6178	447	4	andrzej	andrzej	PROPN
ejpam-6178	447	5	walendziak	walendziak	PROPN
ejpam-6178	447	6	.	.	PUNCT
ejpam-6178	448	1	a	a	DET
ejpam-6178	448	2	note	note	NOUN
ejpam-6178	448	3	on	on	ADP
ejpam-6178	448	4	normal	normal	ADJ
ejpam-6178	448	5	subalgebras	subalgebra	NOUN
ejpam-6178	448	6	in	in	ADP
ejpam-6178	448	7	b	b	NOUN
ejpam-6178	448	8	-	-	PUNCT
ejpam-6178	448	9	algebras	algebras	PROPN
ejpam-6178	448	10	.	.	PUNCT
ejpam-6178	449	1	scientiae	scientiae	PROPN
ejpam-6178	449	2	mathematicae	mathematicae	PROPN
ejpam-6178	449	3	japonicae	japonicae	PROPN
ejpam-6178	449	4	,	,	PUNCT
ejpam-6178	449	5	62	62	NUM
ejpam-6178	449	6	,	,	PUNCT
ejpam-6178	449	7	01	01	NUM
ejpam-6178	449	8	2005	2005	NUM
ejpam-6178	449	9	.	.	PUNCT
ejpam-6178	450	1	[	[	X
ejpam-6178	450	2	7	7	X
ejpam-6178	450	3	]	]	X
ejpam-6178	450	4	joemar	joemar	PROPN
ejpam-6178	450	5	c	c	PROPN
ejpam-6178	450	6	endam	endam	PROPN
ejpam-6178	450	7	and	and	CCONJ
ejpam-6178	450	8	jenette	jenette	PROPN
ejpam-6178	450	9	s	s	PROPN
ejpam-6178	450	10	bantug	bantug	PROPN
ejpam-6178	450	11	.	.	PUNCT
ejpam-6178	451	1	cauchy	cauchy	PROPN
ejpam-6178	451	2	’s	’s	PART
ejpam-6178	451	3	theorem	theorem	NOUN
ejpam-6178	451	4	for	for	ADP
ejpam-6178	451	5	b	b	NOUN
ejpam-6178	451	6	-	-	PUNCT
ejpam-6178	451	7	algebras	algebra	NOUN
ejpam-6178	451	8	.	.	PUNCT
ejpam-6178	452	1	sci	sci	PROPN
ejpam-6178	452	2	.	.	PROPN
ejpam-6178	452	3	math	math	PROPN
ejpam-6178	452	4	.	.	PUNCT
ejpam-6178	453	1	jpn	jpn	PROPN
ejpam-6178	453	2	,	,	PUNCT
ejpam-6178	453	3	82(3):221–228	82(3):221–228	PROPN
ejpam-6178	453	4	,	,	PUNCT
ejpam-6178	453	5	2019	2019	NUM
ejpam-6178	453	6	.	.	PUNCT
ejpam-6178	454	1	[	[	X
ejpam-6178	454	2	8	8	X
ejpam-6178	454	3	]	]	X
ejpam-6178	454	4	j.	j.	PROPN
ejpam-6178	454	5	neggers	neggers	PROPN
ejpam-6178	454	6	.	.	PUNCT
ejpam-6178	455	1	a	a	DET
ejpam-6178	455	2	fundamental	fundamental	ADJ
ejpam-6178	455	3	theorem	theorem	NOUN
ejpam-6178	455	4	of	of	ADP
ejpam-6178	455	5	b	b	NOUN
ejpam-6178	455	6	-	-	PUNCT
ejpam-6178	455	7	homomorphism	homomorphism	NOUN
ejpam-6178	455	8	for	for	ADP
ejpam-6178	455	9	b	b	NOUN
ejpam-6178	455	10	-	-	PUNCT
ejpam-6178	455	11	algebras	algebras	PROPN
ejpam-6178	455	12	.	.	PUNCT
ejpam-6178	455	13	2002	2002	NUM
ejpam-6178	455	14	.	.	PUNCT
ejpam-6178	456	1	[	[	X
ejpam-6178	456	2	9	9	X
ejpam-6178	456	3	]	]	PUNCT
ejpam-6178	456	4	joemar	joemar	PROPN
ejpam-6178	456	5	c	c	PROPN
ejpam-6178	456	6	endam	endam	PROPN
ejpam-6178	456	7	and	and	CCONJ
ejpam-6178	456	8	jocelyn	jocelyn	PROPN
ejpam-6178	456	9	p	p	PROPN
ejpam-6178	456	10	vilela	vilela	PROPN
ejpam-6178	456	11	.	.	PUNCT
ejpam-6178	457	1	the	the	DET
ejpam-6178	457	2	second	second	ADJ
ejpam-6178	457	3	isomorphism	isomorphism	NOUN
ejpam-6178	457	4	theorem	theorem	NOUN
ejpam-6178	457	5	for	for	ADP
ejpam-6178	457	6	balgebras	balgebras	PROPN
ejpam-6178	457	7	.	.	PROPN
ejpam-6178	457	8	applied	apply	VERB
ejpam-6178	457	9	mathematical	mathematical	ADJ
ejpam-6178	457	10	sciences	science	NOUN
ejpam-6178	457	11	,	,	PUNCT
ejpam-6178	457	12	8(38):1865–1872	8(38):1865–1872	NUM
ejpam-6178	457	13	,	,	PUNCT
ejpam-6178	457	14	2014	2014	NUM
ejpam-6178	457	15	.	.	PUNCT
ejpam-6178	458	1	[	[	X
ejpam-6178	458	2	10	10	NUM
ejpam-6178	458	3	]	]	X
ejpam-6178	458	4	katrina	katrina	PROPN
ejpam-6178	458	5	belleza	belleza	PROPN
ejpam-6178	458	6	and	and	CCONJ
ejpam-6178	458	7	jimboy	jimboy	PROPN
ejpam-6178	458	8	albaracin	albaracin	PROPN
ejpam-6178	458	9	.	.	PUNCT
ejpam-6178	459	1	on	on	ADP
ejpam-6178	459	2	dual	dual	ADJ
ejpam-6178	459	3	b	b	NOUN
ejpam-6178	459	4	-	-	PUNCT
ejpam-6178	459	5	filters	filter	NOUN
ejpam-6178	459	6	and	and	CCONJ
ejpam-6178	459	7	dual	dual	ADJ
ejpam-6178	459	8	b	b	NOUN
ejpam-6178	459	9	-	-	PUNCT
ejpam-6178	459	10	subalgebras	subalgebras	PROPN
ejpam-6178	459	11	in	in	ADP
ejpam-6178	459	12	a	a	DET
ejpam-6178	459	13	topological	topological	ADJ
ejpam-6178	459	14	dual	dual	ADJ
ejpam-6178	459	15	b	b	NOUN
ejpam-6178	459	16	-	-	PUNCT
ejpam-6178	459	17	algebra	algebra	NOUN
ejpam-6178	459	18	.	.	PUNCT
ejpam-6178	460	1	journal	journal	NOUN
ejpam-6178	460	2	of	of	ADP
ejpam-6178	460	3	mathematics	mathematic	NOUN
ejpam-6178	460	4	and	and	CCONJ
ejpam-6178	460	5	computer	computer	NOUN
ejpam-6178	460	6	science	science	NOUN
ejpam-6178	460	7	,	,	PUNCT
ejpam-6178	460	8	28:1–10	28:1–10	NUM
ejpam-6178	460	9	,	,	PUNCT
ejpam-6178	460	10	04	04	NUM
ejpam-6178	460	11	2022	2022	NUM
ejpam-6178	460	12	.	.	PUNCT
ejpam-6178	461	1	[	[	X
ejpam-6178	461	2	11	11	NUM
ejpam-6178	461	3	]	]	PUNCT
ejpam-6178	461	4	jethro	jethro	PROPN
ejpam-6178	461	5	elijah	elijah	PROPN
ejpam-6178	461	6	bolima	bolima	PROPN
ejpam-6178	461	7	and	and	CCONJ
ejpam-6178	461	8	katrina	katrina	PROPN
ejpam-6178	461	9	belleza	belleza	PROPN
ejpam-6178	461	10	fuentes	fuentes	PROPN
ejpam-6178	461	11	.	.	PUNCT
ejpam-6178	462	1	first	first	ADV
ejpam-6178	462	2	and	and	CCONJ
ejpam-6178	462	3	third	third	ADJ
ejpam-6178	462	4	isomorphism	isomorphism	NOUN
ejpam-6178	462	5	theorems	theorem	NOUN
ejpam-6178	462	6	for	for	ADP
ejpam-6178	462	7	the	the	DET
ejpam-6178	462	8	dual	dual	ADJ
ejpam-6178	462	9	b	b	NOUN
ejpam-6178	462	10	-	-	PUNCT
ejpam-6178	462	11	algebra	algebra	NOUN
ejpam-6178	462	12	.	.	PUNCT
ejpam-6178	463	1	european	european	ADJ
ejpam-6178	463	2	journal	journal	PROPN
ejpam-6178	463	3	of	of	ADP
ejpam-6178	463	4	pure	pure	ADJ
ejpam-6178	463	5	and	and	CCONJ
ejpam-6178	463	6	applied	applied	ADJ
ejpam-6178	463	7	mathematics	mathematic	NOUN
ejpam-6178	463	8	,	,	PUNCT
ejpam-6178	463	9	16(1):577–586	16(1):577–586	PROPN
ejpam-6178	463	10	,	,	PUNCT
ejpam-6178	463	11	2023	2023	NUM
ejpam-6178	463	12	.	.	PUNCT
ejpam-6178	464	1	[	[	X
ejpam-6178	464	2	12	12	NUM
ejpam-6178	464	3	]	]	X
ejpam-6178	464	4	yuzhong	yuzhong	PROPN
ejpam-6178	464	5	ding	ding	PROPN
ejpam-6178	464	6	,	,	PUNCT
ejpam-6178	464	7	fuguo	fuguo	PROPN
ejpam-6178	464	8	ge	ge	PROPN
ejpam-6178	464	9	,	,	PUNCT
ejpam-6178	464	10	and	and	CCONJ
ejpam-6178	464	11	chenglong	chenglong	PROPN
ejpam-6178	464	12	wu	wu	PROPN
ejpam-6178	464	13	.	.	PUNCT
ejpam-6178	465	1	bci	bci	NOUN
ejpam-6178	465	2	-	-	PUNCT
ejpam-6178	465	3	homomorphisms	homomorphism	NOUN
ejpam-6178	465	4	.	.	PUNCT
ejpam-6178	466	1	formaliz	formaliz	PROPN
ejpam-6178	466	2	.	.	PUNCT
ejpam-6178	467	1	math	math	NOUN
ejpam-6178	467	2	.	.	PUNCT
ejpam-6178	467	3	,	,	PUNCT
ejpam-6178	467	4	16(1	16(1	PROPN
ejpam-6178	467	5	-	-	SYM
ejpam-6178	467	6	4):371–376	4):371–376	NUM
ejpam-6178	467	7	,	,	PUNCT
ejpam-6178	467	8	2008	2008	NUM
ejpam-6178	467	9	.	.	PUNCT
ejpam-6178	468	1	[	[	X
ejpam-6178	468	2	13	13	NUM
ejpam-6178	468	3	]	]	PUNCT
ejpam-6178	468	4	iampan	iampan	NOUN
ejpam-6178	468	5	aiyared	aiyare	VERB
ejpam-6178	468	6	and	and	CCONJ
ejpam-6178	468	7	rajesh	rajesh	PROPN
ejpam-6178	468	8	neelamegarajan	neelamegarajan	PROPN
ejpam-6178	468	9	vanishree	vanishree	PROPN
ejpam-6178	468	10	murugesan	murugesan	PROPN
ejpam-6178	468	11	.	.	PUNCT
ejpam-6178	469	1	the	the	DET
ejpam-6178	469	2	isomorphism	isomorphism	NOUN
ejpam-6178	469	3	theorems	theorem	VERB
ejpam-6178	469	4	for	for	ADP
ejpam-6178	469	5	hilbert	hilbert	PROPN
ejpam-6178	469	6	algebras	algebra	NOUN
ejpam-6178	469	7	.	.	PUNCT
ejpam-6178	470	1	14(12):1243	14(12):1243	NUM
ejpam-6178	470	2	,	,	PUNCT
ejpam-6178	470	3	2023	2023	NUM
ejpam-6178	470	4	.	.	PUNCT
ejpam-6178	471	1	[	[	X
ejpam-6178	471	2	14	14	NUM
ejpam-6178	471	3	]	]	X
ejpam-6178	471	4	cs	cs	PROPN
ejpam-6178	471	5	hoo	hoo	INTJ
ejpam-6178	471	6	.	.	PUNCT
ejpam-6178	472	1	topological	topological	ADJ
ejpam-6178	472	2	mv	mv	PROPN
ejpam-6178	472	3	-	-	PUNCT
ejpam-6178	472	4	algebras	algebra	NOUN
ejpam-6178	472	5	.	.	PUNCT
ejpam-6178	473	1	topology	topology	NOUN
ejpam-6178	473	2	and	and	CCONJ
ejpam-6178	473	3	its	its	PRON
ejpam-6178	473	4	applications	application	NOUN
ejpam-6178	473	5	,	,	PUNCT
ejpam-6178	473	6	81(2):103–121	81(2):103–121	NUM
ejpam-6178	473	7	,	,	PUNCT
ejpam-6178	473	8	1997	1997	NUM
ejpam-6178	473	9	.	.	PUNCT
ejpam-6178	474	1	r.	r.	PROPN
ejpam-6178	474	2	nuñez	nuñez	PROPN
ejpam-6178	474	3	,	,	PUNCT
ejpam-6178	474	4	k.	k.	PROPN
ejpam-6178	474	5	b.	b.	PROPN
ejpam-6178	474	6	fuentes	fuentes	PROPN
ejpam-6178	474	7	/	/	SYM
ejpam-6178	474	8	eur	eur	PROPN
ejpam-6178	474	9	.	.	PUNCT
ejpam-6178	475	1	j.	j.	PROPN
ejpam-6178	475	2	pure	pure	PROPN
ejpam-6178	475	3	appl	appl	PROPN
ejpam-6178	475	4	.	.	PROPN
ejpam-6178	475	5	math	math	PROPN
ejpam-6178	475	6	,	,	PUNCT
ejpam-6178	475	7	18	18	NUM
ejpam-6178	475	8	(	(	PUNCT
ejpam-6178	475	9	4	4	NUM
ejpam-6178	475	10	)	)	PUNCT
ejpam-6178	475	11	(	(	PUNCT
ejpam-6178	475	12	2025	2025	NUM
ejpam-6178	475	13	)	)	PUNCT
ejpam-6178	475	14	,	,	PUNCT
ejpam-6178	475	15	6178	6178	NUM
ejpam-6178	475	16	13	13	NUM
ejpam-6178	475	17	of	of	ADP
ejpam-6178	475	18	15	15	NUM
ejpam-6178	475	19	[	[	SYM
ejpam-6178	475	20	15	15	NUM
ejpam-6178	475	21	]	]	X
ejpam-6178	475	22	narciso	narciso	PROPN
ejpam-6178	475	23	c	c	PROPN
ejpam-6178	475	24	gonzaga	gonzaga	PROPN
ejpam-6178	475	25	jr	jr	PROPN
ejpam-6178	475	26	.	.	PROPN
ejpam-6178	475	27	analyzing	analyze	VERB
ejpam-6178	475	28	some	some	DET
ejpam-6178	475	29	structural	structural	ADJ
ejpam-6178	475	30	properties	property	NOUN
ejpam-6178	475	31	of	of	ADP
ejpam-6178	475	32	topological	topological	ADJ
ejpam-6178	475	33	b	b	PROPN
ejpam-6178	475	34	-	-	PUNCT
ejpam-6178	475	35	algebras	algebras	PROPN
ejpam-6178	475	36	.	.	PUNCT
ejpam-6178	476	1	international	international	ADJ
ejpam-6178	476	2	journal	journal	PROPN
ejpam-6178	476	3	of	of	ADP
ejpam-6178	476	4	mathematics	mathematics	PROPN
ejpam-6178	476	5	and	and	CCONJ
ejpam-6178	476	6	mathematical	mathematical	ADJ
ejpam-6178	476	7	sciences	science	NOUN
ejpam-6178	476	8	,	,	PUNCT
ejpam-6178	476	9	2019(1):8683965	2019(1):8683965	NOUN
ejpam-6178	476	10	,	,	PUNCT
ejpam-6178	476	11	2019	2019	NUM
ejpam-6178	476	12	.	.	PUNCT
ejpam-6178	477	1	[	[	X
ejpam-6178	477	2	16	16	NUM
ejpam-6178	477	3	]	]	PUNCT
ejpam-6178	477	4	akarachai	akarachai	PROPN
ejpam-6178	477	5	satirad	satirad	PROPN
ejpam-6178	477	6	and	and	CCONJ
ejpam-6178	477	7	aiyared	aiyare	VERB
ejpam-6178	477	8	iampan	iampan	PROPN
ejpam-6178	477	9	.	.	PUNCT
ejpam-6178	478	1	topological	topological	ADJ
ejpam-6178	478	2	up	up	ADP
ejpam-6178	478	3	-	-	PUNCT
ejpam-6178	478	4	algebras	algebras	X
ejpam-6178	478	5	.	.	PUNCT
ejpam-6178	479	1	discussiones	discussione	NOUN
ejpam-6178	479	2	mathematicae	mathematicae	PROPN
ejpam-6178	479	3	:	:	PUNCT
ejpam-6178	479	4	general	general	ADJ
ejpam-6178	479	5	algebra	algebra	PROPN
ejpam-6178	479	6	&	&	CCONJ
ejpam-6178	479	7	applications	application	NOUN
ejpam-6178	479	8	,	,	PUNCT
ejpam-6178	479	9	39(2	39(2	NUM
ejpam-6178	479	10	)	)	PUNCT
ejpam-6178	479	11	,	,	PUNCT
ejpam-6178	479	12	2019	2019	NUM
ejpam-6178	479	13	.	.	PUNCT
ejpam-6178	480	1	[	[	X
ejpam-6178	480	2	17	17	NUM
ejpam-6178	480	3	]	]	X
ejpam-6178	480	4	katrina	katrina	PROPN
ejpam-6178	480	5	belleza	belleza	PROPN
ejpam-6178	480	6	and	and	CCONJ
ejpam-6178	480	7	jocelyn	jocelyn	PROPN
ejpam-6178	480	8	p	p	PROPN
ejpam-6178	480	9	vilela	vilela	PROPN
ejpam-6178	480	10	.	.	PUNCT
ejpam-6178	481	1	the	the	DET
ejpam-6178	481	2	dual	dual	ADJ
ejpam-6178	481	3	b	b	NOUN
ejpam-6178	481	4	-	-	PUNCT
ejpam-6178	481	5	algebra	algebra	NOUN
ejpam-6178	481	6	.	.	PUNCT
ejpam-6178	482	1	european	european	ADJ
ejpam-6178	482	2	journal	journal	PROPN
ejpam-6178	482	3	of	of	ADP
ejpam-6178	482	4	pure	pure	ADJ
ejpam-6178	482	5	and	and	CCONJ
ejpam-6178	482	6	applied	applied	ADJ
ejpam-6178	482	7	mathematics	mathematic	NOUN
ejpam-6178	482	8	,	,	PUNCT
ejpam-6178	482	9	12(4):1497–1507	12(4):1497–1507	NUM
ejpam-6178	482	10	,	,	PUNCT
ejpam-6178	482	11	2019	2019	NUM
ejpam-6178	482	12	.	.	PUNCT
ejpam-6178	483	1	[	[	X
ejpam-6178	483	2	18	18	NUM
ejpam-6178	483	3	]	]	X
ejpam-6178	483	4	james	james	PROPN
ejpam-6178	483	5	dugundji	dugundji	PROPN
ejpam-6178	483	6	.	.	PUNCT
ejpam-6178	484	1	topology	topology	PROPN
ejpam-6178	484	2	.	.	PUNCT
ejpam-6178	485	1	boston	boston	PROPN
ejpam-6178	485	2	,	,	PUNCT
ejpam-6178	485	3	mass	mass	PROPN
ejpam-6178	485	4	,	,	PUNCT
ejpam-6178	485	5	1966	1966	NUM
ejpam-6178	485	6	.	.	PUNCT
ejpam-6178	486	1	[	[	X
ejpam-6178	486	2	19	19	NUM
ejpam-6178	486	3	]	]	X
ejpam-6178	486	4	s.	s.	PROPN
ejpam-6178	486	5	lipschutz	lipschutz	PROPN
ejpam-6178	486	6	.	.	PUNCT
ejpam-6178	487	1	schaum	schaum	PROPN
ejpam-6178	487	2	’s	’s	PART
ejpam-6178	487	3	outline	outline	NOUN
ejpam-6178	487	4	of	of	ADP
ejpam-6178	487	5	general	general	ADJ
ejpam-6178	487	6	topology	topology	NOUN
ejpam-6178	487	7	.	.	PUNCT
ejpam-6178	488	1	schaum	schaum	PROPN
ejpam-6178	488	2	’s	’s	PART
ejpam-6178	488	3	outline	outline	PROPN
ejpam-6178	488	4	series	series	PROPN
ejpam-6178	488	5	in	in	ADP
ejpam-6178	488	6	mathematics	mathematics	PROPN
ejpam-6178	488	7	.	.	PUNCT
ejpam-6178	489	1	mcgraw	mcgraw	PROPN
ejpam-6178	489	2	-	-	PUNCT
ejpam-6178	489	3	hill	hill	NOUN
ejpam-6178	489	4	companies	company	NOUN
ejpam-6178	489	5	,	,	PUNCT
ejpam-6178	489	6	incorporated	incorporate	VERB
ejpam-6178	489	7	,	,	PUNCT
ejpam-6178	489	8	1965	1965	NUM
ejpam-6178	489	9	.	.	PUNCT
ejpam-6178	490	1	appendix	appendix	VERB
ejpam-6178	490	2	verification	verification	NOUN
ejpam-6178	490	3	that	that	SCONJ
ejpam-6178	490	4	the	the	DET
ejpam-6178	490	5	(	(	PUNCT
ejpam-6178	490	6	x	x	SYM
ejpam-6178	490	7	/	/	SYM
ejpam-6178	490	8	s	s	PROPN
ejpam-6178	490	9	,	,	PUNCT
ejpam-6178	490	10	∗	∗	NOUN
ejpam-6178	490	11	,	,	PUNCT
ejpam-6178	490	12	τs	τs	NOUN
ejpam-6178	490	13	)	)	PUNCT
ejpam-6178	490	14	in	in	ADP
ejpam-6178	490	15	example	example	NOUN
ejpam-6178	490	16	3	3	NUM
ejpam-6178	490	17	is	be	AUX
ejpam-6178	490	18	a	a	DET
ejpam-6178	490	19	tdb	tdb	PROPN
ejpam-6178	490	20	-	-	NOUN
ejpam-6178	490	21	algebra	algebra	NOUN
ejpam-6178	490	22	consider	consider	VERB
ejpam-6178	490	23	the	the	DET
ejpam-6178	490	24	tdb	tdb	NOUN
ejpam-6178	490	25	-	-	NOUN
ejpam-6178	490	26	algebra	algebra	NOUN
ejpam-6178	490	27	in	in	ADP
ejpam-6178	490	28	example	example	NOUN
ejpam-6178	490	29	2	2	NUM
ejpam-6178	490	30	.	.	X
ejpam-6178	491	1	that	that	PRON
ejpam-6178	491	2	is	be	AUX
ejpam-6178	491	3	the	the	DET
ejpam-6178	491	4	db	db	NOUN
ejpam-6178	491	5	-	-	PUNCT
ejpam-6178	491	6	algebra	algebra	NOUN
ejpam-6178	491	7	x	x	PUNCT
ejpam-6178	491	8	=	=	SYM
ejpam-6178	491	9	{	{	PUNCT
ejpam-6178	491	10	1	1	NUM
ejpam-6178	491	11	,	,	PUNCT
ejpam-6178	491	12	a	a	DET
ejpam-6178	491	13	,	,	PUNCT
ejpam-6178	491	14	b	b	NOUN
ejpam-6178	491	15	,	,	PUNCT
ejpam-6178	491	16	c	c	NOUN
ejpam-6178	491	17	}	}	PUNCT
ejpam-6178	491	18	with	with	ADP
ejpam-6178	491	19	binary	binary	ADJ
ejpam-6178	491	20	operation	operation	NOUN
ejpam-6178	491	21	“	"	PUNCT
ejpam-6178	491	22	◦	◦	NOUN
ejpam-6178	491	23	”	"	PUNCT
ejpam-6178	491	24	as	as	SCONJ
ejpam-6178	491	25	defined	define	VERB
ejpam-6178	491	26	by	by	ADP
ejpam-6178	491	27	the	the	DET
ejpam-6178	491	28	cayley	cayley	ADJ
ejpam-6178	491	29	table	table	NOUN
ejpam-6178	491	30	below	below	ADV
ejpam-6178	491	31	,	,	PUNCT
ejpam-6178	491	32	◦	◦	VERB
ejpam-6178	491	33	1	1	NUM
ejpam-6178	491	34	a	a	DET
ejpam-6178	491	35	b	b	NOUN
ejpam-6178	491	36	c	c	NOUN
ejpam-6178	491	37	1	1	NUM
ejpam-6178	491	38	1	1	NUM
ejpam-6178	491	39	a	a	DET
ejpam-6178	491	40	b	b	NOUN
ejpam-6178	491	41	c	c	ADP
ejpam-6178	491	42	a	a	DET
ejpam-6178	491	43	a	a	DET
ejpam-6178	491	44	1	1	NUM
ejpam-6178	491	45	c	c	NOUN
ejpam-6178	491	46	b	b	PROPN
ejpam-6178	491	47	b	b	PROPN
ejpam-6178	491	48	b	b	PROPN
ejpam-6178	491	49	c	c	PROPN
ejpam-6178	491	50	1	1	NUM
ejpam-6178	491	51	a	a	DET
ejpam-6178	491	52	c	c	NOUN
ejpam-6178	491	53	c	c	NOUN
ejpam-6178	491	54	b	b	PROPN
ejpam-6178	491	55	a	a	DET
ejpam-6178	491	56	1	1	NUM
ejpam-6178	491	57	and	and	CCONJ
ejpam-6178	491	58	a	a	DET
ejpam-6178	491	59	topology	topology	NOUN
ejpam-6178	491	60	τ	τ	X
ejpam-6178	491	61	=	=	SYM
ejpam-6178	491	62	{	{	PUNCT
ejpam-6178	491	63	x,∅	x,∅	PROPN
ejpam-6178	491	64	,	,	PUNCT
ejpam-6178	491	65	{	{	PUNCT
ejpam-6178	491	66	1	1	NUM
ejpam-6178	491	67	,	,	PUNCT
ejpam-6178	491	68	a	a	PRON
ejpam-6178	491	69	}	}	PUNCT
ejpam-6178	491	70	,	,	PUNCT
ejpam-6178	491	71	{	{	PUNCT
ejpam-6178	491	72	b	b	X
ejpam-6178	491	73	,	,	PUNCT
ejpam-6178	491	74	c	c	NOUN
ejpam-6178	491	75	}	}	PUNCT
ejpam-6178	491	76	}	}	PUNCT
ejpam-6178	491	77	.	.	PUNCT
ejpam-6178	492	1	note	note	VERB
ejpam-6178	492	2	that	that	SCONJ
ejpam-6178	492	3	s	s	VERB
ejpam-6178	492	4	=	=	X
ejpam-6178	492	5	{	{	PUNCT
ejpam-6178	492	6	1	1	NUM
ejpam-6178	492	7	}	}	PUNCT
ejpam-6178	492	8	is	be	AUX
ejpam-6178	492	9	a	a	DET
ejpam-6178	492	10	normal	normal	ADJ
ejpam-6178	492	11	db	db	NOUN
ejpam-6178	492	12	-	-	PUNCT
ejpam-6178	492	13	subalgebra	subalgebra	NOUN
ejpam-6178	492	14	of	of	ADP
ejpam-6178	492	15	x.	x.	NOUN
ejpam-6178	492	16	also	also	ADV
ejpam-6178	492	17	,	,	PUNCT
ejpam-6178	493	1	[	[	X
ejpam-6178	493	2	1]s	1]s	NUM
ejpam-6178	493	3	=	=	SYM
ejpam-6178	493	4	{	{	PUNCT
ejpam-6178	493	5	1	1	NUM
ejpam-6178	493	6	}	}	PUNCT
ejpam-6178	493	7	,	,	PUNCT
ejpam-6178	493	8	[	[	X
ejpam-6178	493	9	a]s	a]s	NOUN
ejpam-6178	493	10	=	=	SYM
ejpam-6178	493	11	{	{	PUNCT
ejpam-6178	493	12	a	a	NOUN
ejpam-6178	493	13	}	}	PUNCT
ejpam-6178	493	14	,	,	PUNCT
ejpam-6178	493	15	[	[	X
ejpam-6178	493	16	b]s	b]s	NOUN
ejpam-6178	493	17	=	=	PUNCT
ejpam-6178	493	18	{	{	PUNCT
ejpam-6178	493	19	b	b	NOUN
ejpam-6178	493	20	}	}	PUNCT
ejpam-6178	493	21	,	,	PUNCT
ejpam-6178	493	22	[	[	X
ejpam-6178	493	23	c]s	c]s	NOUN
ejpam-6178	493	24	=	=	SYM
ejpam-6178	493	25	{	{	PUNCT
ejpam-6178	493	26	c	c	NOUN
ejpam-6178	493	27	}	}	PUNCT
ejpam-6178	493	28	.	.	PUNCT
ejpam-6178	494	1	then	then	ADV
ejpam-6178	494	2	x	x	X
ejpam-6178	494	3	/	/	SYM
ejpam-6178	494	4	s	s	NOUN
ejpam-6178	494	5	=	=	X
ejpam-6178	494	6	{	{	PUNCT
ejpam-6178	494	7	[	[	X
ejpam-6178	494	8	1]s	1]s	NOUN
ejpam-6178	494	9	,	,	PUNCT
ejpam-6178	494	10	[	[	X
ejpam-6178	494	11	a]s	a]s	ADJ
ejpam-6178	494	12	,	,	PUNCT
ejpam-6178	494	13	[	[	X
ejpam-6178	494	14	b]s	b]s	NOUN
ejpam-6178	494	15	,	,	PUNCT
ejpam-6178	494	16	[	[	X
ejpam-6178	494	17	c]s	c]s	NOUN
ejpam-6178	494	18	}	}	PUNCT
ejpam-6178	494	19	.	.	PUNCT
ejpam-6178	495	1	hence	hence	ADV
ejpam-6178	495	2	,	,	PUNCT
ejpam-6178	495	3	τs	τs	X
ejpam-6178	495	4	=	=	SYM
ejpam-6178	495	5	{	{	PUNCT
ejpam-6178	495	6	x	x	X
ejpam-6178	495	7	/	/	SYM
ejpam-6178	495	8	s,∅	s,∅	NOUN
ejpam-6178	495	9	,	,	PUNCT
ejpam-6178	495	10	{	{	PUNCT
ejpam-6178	495	11	[	[	X
ejpam-6178	495	12	1]s	1]s	NOUN
ejpam-6178	495	13	,	,	PUNCT
ejpam-6178	495	14	[	[	X
ejpam-6178	495	15	a]s	a]s	ADV
ejpam-6178	495	16	}	}	PUNCT
ejpam-6178	495	17	,	,	PUNCT
ejpam-6178	495	18	{	{	PUNCT
ejpam-6178	496	1	[	[	X
ejpam-6178	496	2	b]s	b]s	NOUN
ejpam-6178	496	3	,	,	PUNCT
ejpam-6178	496	4	[	[	X
ejpam-6178	496	5	c]s	c]s	NOUN
ejpam-6178	496	6	}	}	PUNCT
ejpam-6178	496	7	}	}	PUNCT
ejpam-6178	496	8	.	.	PUNCT
ejpam-6178	497	1	hence	hence	ADV
ejpam-6178	497	2	,	,	PUNCT
ejpam-6178	497	3	the	the	DET
ejpam-6178	497	4	cayley	cayley	ADJ
ejpam-6178	497	5	table	table	NOUN
ejpam-6178	497	6	for	for	ADP
ejpam-6178	497	7	the	the	DET
ejpam-6178	497	8	operation	operation	NOUN
ejpam-6178	497	9	defined	define	VERB
ejpam-6178	497	10	on	on	ADP
ejpam-6178	497	11	x	x	X
ejpam-6178	497	12	/	/	SYM
ejpam-6178	497	13	s	s	PART
ejpam-6178	497	14	is	be	AUX
ejpam-6178	497	15	described	describe	VERB
ejpam-6178	497	16	below	below	ADP
ejpam-6178	497	17	:	:	PUNCT
ejpam-6178	497	18	∗	∗	NOUN
ejpam-6178	498	1	[	[	X
ejpam-6178	498	2	1]s	1]s	NUM
ejpam-6178	498	3	[	[	X
ejpam-6178	498	4	a]s	a]s	NOUN
ejpam-6178	499	1	[	[	X
ejpam-6178	499	2	b]s	b]s	NOUN
ejpam-6178	499	3	[	[	X
ejpam-6178	499	4	c]s	c]s	X
ejpam-6178	500	1	[	[	X
ejpam-6178	501	1	1]s	1]s	NOUN
ejpam-6178	501	2	[	[	X
ejpam-6178	501	3	1]s	1]s	NOUN
ejpam-6178	501	4	[	[	X
ejpam-6178	501	5	a]s	a]s	NOUN
ejpam-6178	502	1	[	[	X
ejpam-6178	502	2	b]s	b]s	NOUN
ejpam-6178	502	3	[	[	X
ejpam-6178	502	4	c]s	c]s	X
ejpam-6178	503	1	[	[	X
ejpam-6178	503	2	a]s	a]s	X
ejpam-6178	504	1	[	[	X
ejpam-6178	504	2	a]s	a]s	NOUN
ejpam-6178	504	3	[	[	X
ejpam-6178	504	4	1]s	1]s	NUM
ejpam-6178	504	5	[	[	X
ejpam-6178	504	6	c]s	c]s	NOUN
ejpam-6178	504	7	[	[	X
ejpam-6178	504	8	b]s	b]s	NOUN
ejpam-6178	505	1	[	[	X
ejpam-6178	505	2	b]s	b]s	NOUN
ejpam-6178	506	1	[	[	X
ejpam-6178	506	2	b]s	b]s	NOUN
ejpam-6178	506	3	[	[	X
ejpam-6178	506	4	c]s	c]s	X
ejpam-6178	507	1	[	[	X
ejpam-6178	507	2	1]s	1]s	NOUN
ejpam-6178	507	3	[	[	X
ejpam-6178	507	4	a]s	a]s	NOUN
ejpam-6178	508	1	[	[	X
ejpam-6178	508	2	c]s	c]s	NOUN
ejpam-6178	508	3	[	[	X
ejpam-6178	508	4	c]s	c]s	NOUN
ejpam-6178	508	5	[	[	X
ejpam-6178	508	6	b]s	b]s	NOUN
ejpam-6178	508	7	[	[	X
ejpam-6178	508	8	a]s	a]s	ADJ
ejpam-6178	508	9	[	[	X
ejpam-6178	508	10	1]s	1]s	NOUN
ejpam-6178	508	11	now	now	ADV
ejpam-6178	508	12	,	,	PUNCT
ejpam-6178	508	13	observed	observe	VERB
ejpam-6178	508	14	that	that	SCONJ
ejpam-6178	508	15	∗−1(x	∗−1(x	PROPN
ejpam-6178	508	16	/	/	SYM
ejpam-6178	508	17	s	s	NOUN
ejpam-6178	508	18	)	)	PUNCT
ejpam-6178	508	19	=	=	SYM
ejpam-6178	509	1	x	x	X
ejpam-6178	509	2	/	/	SYM
ejpam-6178	509	3	s	s	NOUN
ejpam-6178	509	4	×x	×x	X
ejpam-6178	509	5	/	/	SYM
ejpam-6178	509	6	s	s	PART
ejpam-6178	509	7	∗−1(∅	∗−1(∅	NOUN
ejpam-6178	509	8	)	)	PUNCT
ejpam-6178	509	9	=	=	SYM
ejpam-6178	509	10	∅×∅	∅×∅	NOUN
ejpam-6178	509	11	∗−1({[1]s	∗−1({[1]s	NOUN
ejpam-6178	509	12	,	,	PUNCT
ejpam-6178	509	13	[	[	X
ejpam-6178	509	14	a]s	a]s	ADJ
ejpam-6178	509	15	}	}	PUNCT
ejpam-6178	509	16	)	)	PUNCT
ejpam-6178	509	17	=	=	SYM
ejpam-6178	509	18	(	(	PUNCT
ejpam-6178	509	19	{	{	PUNCT
ejpam-6178	509	20	[	[	X
ejpam-6178	509	21	1]s	1]s	NOUN
ejpam-6178	509	22	,	,	PUNCT
ejpam-6178	509	23	[	[	X
ejpam-6178	509	24	a]s	a]s	ADJ
ejpam-6178	509	25	}	}	PUNCT
ejpam-6178	509	26	×	×	NOUN
ejpam-6178	509	27	{	{	PUNCT
ejpam-6178	509	28	[	[	X
ejpam-6178	509	29	1]s	1]s	NOUN
ejpam-6178	509	30	,	,	PUNCT
ejpam-6178	509	31	[	[	X
ejpam-6178	509	32	a]s	a]s	ADJ
ejpam-6178	509	33	}	}	PUNCT
ejpam-6178	509	34	)	)	PUNCT
ejpam-6178	509	35	∪	∪	X
ejpam-6178	509	36	(	(	PUNCT
ejpam-6178	509	37	{	{	PUNCT
ejpam-6178	509	38	[	[	X
ejpam-6178	509	39	b]s	b]s	NOUN
ejpam-6178	509	40	,	,	PUNCT
ejpam-6178	509	41	[	[	X
ejpam-6178	509	42	c]s	c]s	ADJ
ejpam-6178	509	43	}	}	PUNCT
ejpam-6178	509	44	×	×	NOUN
ejpam-6178	509	45	{	{	PUNCT
ejpam-6178	509	46	[	[	X
ejpam-6178	509	47	b]s	b]s	NOUN
ejpam-6178	509	48	,	,	PUNCT
ejpam-6178	509	49	[	[	X
ejpam-6178	509	50	c]s	c]s	NOUN
ejpam-6178	509	51	}	}	PUNCT
ejpam-6178	509	52	)	)	PUNCT
ejpam-6178	509	53	∗−1({[b]s	∗−1({[b]s	ADJ
ejpam-6178	509	54	,	,	PUNCT
ejpam-6178	509	55	[	[	X
ejpam-6178	509	56	c]s	c]s	NOUN
ejpam-6178	509	57	}	}	PUNCT
ejpam-6178	509	58	}	}	PUNCT
ejpam-6178	509	59	)	)	PUNCT
ejpam-6178	509	60	=	=	SYM
ejpam-6178	509	61	(	(	PUNCT
ejpam-6178	509	62	{	{	PUNCT
ejpam-6178	509	63	[	[	X
ejpam-6178	509	64	1]s	1]s	NOUN
ejpam-6178	509	65	,	,	PUNCT
ejpam-6178	509	66	[	[	X
ejpam-6178	509	67	a]s	a]s	ADJ
ejpam-6178	509	68	}	}	PUNCT
ejpam-6178	509	69	×	×	NOUN
ejpam-6178	509	70	{	{	PUNCT
ejpam-6178	509	71	[	[	X
ejpam-6178	509	72	b]s	b]s	NOUN
ejpam-6178	509	73	,	,	PUNCT
ejpam-6178	509	74	[	[	X
ejpam-6178	509	75	c]s	c]s	NOUN
ejpam-6178	509	76	}	}	PUNCT
ejpam-6178	509	77	}	}	PUNCT
ejpam-6178	509	78	∪	∪	X
ejpam-6178	509	79	(	(	PUNCT
ejpam-6178	509	80	{	{	PUNCT
ejpam-6178	509	81	[	[	X
ejpam-6178	509	82	b]s	b]s	NOUN
ejpam-6178	509	83	,	,	PUNCT
ejpam-6178	509	84	[	[	X
ejpam-6178	509	85	c]s	c]s	ADJ
ejpam-6178	509	86	}	}	PUNCT
ejpam-6178	509	87	×	×	NOUN
ejpam-6178	509	88	{	{	PUNCT
ejpam-6178	509	89	[	[	X
ejpam-6178	509	90	1]s	1]s	NOUN
ejpam-6178	509	91	,	,	PUNCT
ejpam-6178	509	92	[	[	X
ejpam-6178	509	93	a]s	a]s	ADJ
ejpam-6178	509	94	}	}	PUNCT
ejpam-6178	509	95	)	)	PUNCT
ejpam-6178	509	96	they	they	PRON
ejpam-6178	509	97	are	be	AUX
ejpam-6178	509	98	all	all	ADV
ejpam-6178	509	99	basic	basic	ADJ
ejpam-6178	509	100	open	open	ADJ
ejpam-6178	509	101	sets	set	NOUN
ejpam-6178	509	102	for	for	ADP
ejpam-6178	509	103	x×x	x×x	PROPN
ejpam-6178	509	104	.	.	PUNCT
ejpam-6178	510	1	hence	hence	ADV
ejpam-6178	510	2	,	,	PUNCT
ejpam-6178	510	3	∗	∗	NOUN
ejpam-6178	510	4	is	be	AUX
ejpam-6178	510	5	continuous	continuous	ADJ
ejpam-6178	510	6	,	,	PUNCT
ejpam-6178	510	7	it	it	PRON
ejpam-6178	510	8	follows	follow	VERB
ejpam-6178	510	9	that	that	SCONJ
ejpam-6178	510	10	(	(	PUNCT
ejpam-6178	510	11	x	x	X
ejpam-6178	510	12	/	/	SYM
ejpam-6178	510	13	s	s	PROPN
ejpam-6178	510	14	,	,	PUNCT
ejpam-6178	510	15	∗	∗	NOUN
ejpam-6178	510	16	,	,	PUNCT
ejpam-6178	510	17	τs	τs	NOUN
ejpam-6178	510	18	)	)	PUNCT
ejpam-6178	510	19	is	be	AUX
ejpam-6178	510	20	a	a	DET
ejpam-6178	510	21	tdb	tdb	NOUN
ejpam-6178	510	22	-	-	NOUN
ejpam-6178	510	23	algebra	algebra	NOUN
ejpam-6178	510	24	.	.	PUNCT
ejpam-6178	511	1	r.	r.	PROPN
ejpam-6178	511	2	nuñez	nuñez	PROPN
ejpam-6178	511	3	,	,	PUNCT
ejpam-6178	511	4	k.	k.	PROPN
ejpam-6178	511	5	b.	b.	PROPN
ejpam-6178	511	6	fuentes	fuentes	PROPN
ejpam-6178	511	7	/	/	SYM
ejpam-6178	511	8	eur	eur	PROPN
ejpam-6178	511	9	.	.	PUNCT
ejpam-6178	512	1	j.	j.	PROPN
ejpam-6178	512	2	pure	pure	PROPN
ejpam-6178	512	3	appl	appl	PROPN
ejpam-6178	512	4	.	.	PROPN
ejpam-6178	512	5	math	math	PROPN
ejpam-6178	512	6	,	,	PUNCT
ejpam-6178	512	7	18	18	NUM
ejpam-6178	512	8	(	(	PUNCT
ejpam-6178	512	9	4	4	NUM
ejpam-6178	512	10	)	)	PUNCT
ejpam-6178	512	11	(	(	PUNCT
ejpam-6178	512	12	2025	2025	NUM
ejpam-6178	512	13	)	)	PUNCT
ejpam-6178	512	14	,	,	PUNCT
ejpam-6178	512	15	6178	6178	NUM
ejpam-6178	512	16	14	14	NUM
ejpam-6178	512	17	of	of	ADP
ejpam-6178	512	18	15	15	NUM
ejpam-6178	512	19	python	python	NOUN
ejpam-6178	512	20	program	program	NOUN
ejpam-6178	512	21	to	to	PART
ejpam-6178	512	22	verify	verify	VERB
ejpam-6178	512	23	the	the	DET
ejpam-6178	512	24	tdb	tdb	PROPN
ejpam-6178	512	25	-	-	NOUN
ejpam-6178	512	26	homomorphism	homomorphism	NOUN
ejpam-6178	512	27	in	in	ADP
ejpam-6178	512	28	example	example	NOUN
ejpam-6178	512	29	5	5	NUM
ejpam-6178	512	30	class	class	NOUN
ejpam-6178	512	31	algebra	algebra	NOUN
ejpam-6178	512	32	:	:	PUNCT
ejpam-6178	512	33	def	def	VERB
ejpam-6178	512	34	_	_	PUNCT
ejpam-6178	513	1	_	_	PUNCT
ejpam-6178	513	2	init	init	X
ejpam-6178	513	3	_	_	PUNCT
ejpam-6178	514	1	_	_	PUNCT
ejpam-6178	514	2	(	(	PUNCT
ejpam-6178	514	3	s	s	X
ejpam-6178	514	4	e	e	X
ejpam-6178	514	5	l	l	NOUN
ejpam-6178	514	6	f	f	PROPN
ejpam-6178	514	7	,	,	PUNCT
ejpam-6178	514	8	e	e	PROPN
ejpam-6178	514	9	lements	lement	NOUN
ejpam-6178	514	10	,	,	PUNCT
ejpam-6178	514	11	cay	cay	NOUN
ejpam-6178	514	12	ley_table	ley_table	ADV
ejpam-6178	514	13	)	)	PUNCT
ejpam-6178	514	14	:	:	PUNCT
ejpam-6178	514	15	s	s	X
ejpam-6178	514	16	e	e	X
ejpam-6178	514	17	l	l	NOUN
ejpam-6178	514	18	f	f	PROPN
ejpam-6178	514	19	.	.	PUNCT
ejpam-6178	515	1	e	e	NOUN
ejpam-6178	515	2	lements	lement	NOUN
ejpam-6178	515	3	=	=	SYM
ejpam-6178	515	4	elements	element	NOUN
ejpam-6178	515	5	s	s	PART
ejpam-6178	515	6	e	e	NOUN
ejpam-6178	515	7	l	l	NOUN
ejpam-6178	515	8	f	f	PROPN
ejpam-6178	515	9	.	.	PUNCT
ejpam-6178	516	1	cay	cay	PROPN
ejpam-6178	516	2	ley_table	ley_table	PART
ejpam-6178	516	3	=	=	PUNCT
ejpam-6178	516	4	cay	cay	PROPN
ejpam-6178	516	5	ley_table	ley_table	ADJ
ejpam-6178	516	6	def	def	ADJ
ejpam-6178	516	7	operat	operat	NOUN
ejpam-6178	516	8	ion	ion	NOUN
ejpam-6178	516	9	(	(	PUNCT
ejpam-6178	516	10	s	s	X
ejpam-6178	516	11	e	e	X
ejpam-6178	516	12	l	l	NOUN
ejpam-6178	516	13	f	f	PROPN
ejpam-6178	516	14	,	,	PUNCT
ejpam-6178	516	15	a	a	DET
ejpam-6178	516	16	,	,	PUNCT
ejpam-6178	516	17	b	b	NOUN
ejpam-6178	516	18	)	)	PUNCT
ejpam-6178	516	19	:	:	PUNCT
ejpam-6178	516	20	index_a	index_a	X
ejpam-6178	516	21	=	=	SYM
ejpam-6178	516	22	s	s	X
ejpam-6178	516	23	e	e	X
ejpam-6178	516	24	l	l	NOUN
ejpam-6178	516	25	f	f	PROPN
ejpam-6178	516	26	.	.	PUNCT
ejpam-6178	517	1	e	e	NOUN
ejpam-6178	517	2	lements	lement	NOUN
ejpam-6178	517	3	.	.	PUNCT
ejpam-6178	518	1	index	index	NOUN
ejpam-6178	518	2	(	(	PUNCT
ejpam-6178	518	3	a	a	PRON
ejpam-6178	518	4	)	)	PUNCT
ejpam-6178	518	5	index_b	index_b	NOUN
ejpam-6178	518	6	=	=	SYM
ejpam-6178	518	7	s	s	X
ejpam-6178	518	8	e	e	X
ejpam-6178	518	9	l	l	NOUN
ejpam-6178	518	10	f	f	PROPN
ejpam-6178	518	11	.	.	PUNCT
ejpam-6178	519	1	e	e	NOUN
ejpam-6178	519	2	lements	lement	NOUN
ejpam-6178	519	3	.	.	PUNCT
ejpam-6178	520	1	index	index	NOUN
ejpam-6178	520	2	(	(	PUNCT
ejpam-6178	520	3	b	b	NOUN
ejpam-6178	520	4	)	)	PUNCT
ejpam-6178	520	5	return	return	NOUN
ejpam-6178	520	6	s	s	PART
ejpam-6178	520	7	e	e	NOUN
ejpam-6178	520	8	l	l	NOUN
ejpam-6178	520	9	f	f	PROPN
ejpam-6178	520	10	.	.	PUNCT
ejpam-6178	521	1	cay	cay	PROPN
ejpam-6178	521	2	ley_table	ley_table	ADV
ejpam-6178	521	3	[	[	PUNCT
ejpam-6178	521	4	index_a	index_a	X
ejpam-6178	521	5	]	]	PUNCT
ejpam-6178	521	6	[	[	PUNCT
ejpam-6178	521	7	index_b	index_b	NOUN
ejpam-6178	521	8	]	]	PUNCT
ejpam-6178	521	9	def	def	VERB
ejpam-6178	521	10	is_homomorphism	is_homomorphism	NOUN
ejpam-6178	521	11	(	(	PUNCT
ejpam-6178	521	12	h	h	NOUN
ejpam-6178	521	13	,	,	PUNCT
ejpam-6178	521	14	algebra_a	algebra_a	NOUN
ejpam-6178	521	15	,	,	PUNCT
ejpam-6178	521	16	algebra_b	algebra_b	X
ejpam-6178	521	17	)	)	PUNCT
ejpam-6178	521	18	:	:	PUNCT
ejpam-6178	521	19	for	for	ADP
ejpam-6178	521	20	a	a	PRON
ejpam-6178	521	21	in	in	ADP
ejpam-6178	521	22	algebra_a	algebra_a	NOUN
ejpam-6178	521	23	.	.	PUNCT
ejpam-6178	522	1	e	e	NOUN
ejpam-6178	522	2	lements	lement	VERB
ejpam-6178	522	3	:	:	PUNCT
ejpam-6178	522	4	for	for	ADP
ejpam-6178	522	5	b	b	NOUN
ejpam-6178	522	6	in	in	ADP
ejpam-6178	522	7	algebra_a	algebra_a	NOUN
ejpam-6178	522	8	.	.	PUNCT
ejpam-6178	523	1	e	e	NOUN
ejpam-6178	523	2	lements	lement	NOUN
ejpam-6178	523	3	:	:	PUNCT
ejpam-6178	524	1	l	l	X
ejpam-6178	524	2	e	e	NOUN
ejpam-6178	524	3	f	f	PROPN
ejpam-6178	524	4	t	t	PROPN
ejpam-6178	524	5	_	_	PUNCT
ejpam-6178	524	6	s	s	VERB
ejpam-6178	524	7	i	i	NOUN
ejpam-6178	524	8	d	d	X
ejpam-6178	524	9	e	e	NOUN
ejpam-6178	524	10	=	=	SYM
ejpam-6178	524	11	h	h	PROPN
ejpam-6178	524	12	(	(	PUNCT
ejpam-6178	524	13	algebra_a	algebra_a	NOUN
ejpam-6178	524	14	.	.	PUNCT
ejpam-6178	525	1	opera	opera	NOUN
ejpam-6178	525	2	t	t	PROPN
ejpam-6178	525	3	i	i	PRON
ejpam-6178	525	4	on	on	ADP
ejpam-6178	525	5	(	(	PUNCT
ejpam-6178	525	6	a	a	DET
ejpam-6178	525	7	,	,	PUNCT
ejpam-6178	525	8	b	b	NOUN
ejpam-6178	525	9	)	)	PUNCT
ejpam-6178	525	10	)	)	PUNCT
ejpam-6178	526	1	r	r	NOUN
ejpam-6178	527	1	i	i	PRON
ejpam-6178	527	2	gh	gh	PROPN
ejpam-6178	527	3	t_s	t_s	PROPN
ejpam-6178	527	4	ide	ide	NOUN
ejpam-6178	527	5	=	=	NOUN
ejpam-6178	527	6	algebra_b	algebra_b	ADJ
ejpam-6178	527	7	.	.	PUNCT
ejpam-6178	528	1	opera	opera	NOUN
ejpam-6178	528	2	t	t	PROPN
ejpam-6178	528	3	i	i	PRON
ejpam-6178	528	4	on	on	ADP
ejpam-6178	528	5	(	(	PUNCT
ejpam-6178	528	6	h	h	NOUN
ejpam-6178	528	7	(	(	PUNCT
ejpam-6178	528	8	a	a	NOUN
ejpam-6178	528	9	)	)	PUNCT
ejpam-6178	528	10	,	,	PUNCT
ejpam-6178	528	11	h	h	NOUN
ejpam-6178	528	12	(	(	PUNCT
ejpam-6178	528	13	b	b	NOUN
ejpam-6178	528	14	)	)	PUNCT
ejpam-6178	528	15	)	)	PUNCT
ejpam-6178	529	1	i	i	PRON
ejpam-6178	529	2	f	f	X
ejpam-6178	529	3	l	l	NOUN
ejpam-6178	529	4	e	e	X
ejpam-6178	529	5	f	f	PROPN
ejpam-6178	529	6	t	t	PROPN
ejpam-6178	530	1	_	_	PUNCT
ejpam-6178	531	1	s	s	VERB
ejpam-6178	531	2	i	i	NOUN
ejpam-6178	531	3	d	d	NOUN
ejpam-6178	531	4	e	e	NOUN
ejpam-6178	531	5	!	!	PUNCT
ejpam-6178	531	6	=	=	PUNCT
ejpam-6178	532	1	r	r	NOUN
ejpam-6178	532	2	i	i	PROPN
ejpam-6178	532	3	gh	gh	PROPN
ejpam-6178	532	4	t_s	t_s	PROPN
ejpam-6178	532	5	ide	ide	NOUN
ejpam-6178	532	6	:	:	PUNCT
ejpam-6178	532	7	return	return	VERB
ejpam-6178	532	8	false	false	ADJ
ejpam-6178	532	9	return	return	NOUN
ejpam-6178	532	10	true	true	ADJ
ejpam-6178	532	11	elements_a	elements_a	NOUN
ejpam-6178	532	12	=	=	PUNCT
ejpam-6178	532	13	[	[	PUNCT
ejpam-6178	532	14	’	'	PUNCT
ejpam-6178	532	15	a	a	PRON
ejpam-6178	532	16	’	'	PUNCT
ejpam-6178	532	17	,	,	PUNCT
ejpam-6178	532	18	’	'	PUNCT
ejpam-6178	532	19	b	b	X
ejpam-6178	532	20	’	'	PUNCT
ejpam-6178	532	21	,	,	PUNCT
ejpam-6178	532	22	’	'	PUNCT
ejpam-6178	532	23	c	c	X
ejpam-6178	532	24	’	'	PUNCT
ejpam-6178	532	25	,	,	PUNCT
ejpam-6178	532	26	’	'	PUNCT
ejpam-6178	532	27	d	d	X
ejpam-6178	532	28	’	'	PUNCT
ejpam-6178	532	29	]	]	PUNCT
ejpam-6178	532	30	cayley_table_a	cayley_table_a	NOUN
ejpam-6178	533	1	=	=	PUNCT
ejpam-6178	533	2	[	[	PUNCT
ejpam-6178	533	3	[	[	PUNCT
ejpam-6178	533	4	’	'	PUNCT
ejpam-6178	533	5	a	a	PRON
ejpam-6178	533	6	’	'	PUNCT
ejpam-6178	533	7	,	,	PUNCT
ejpam-6178	533	8	’	'	PUNCT
ejpam-6178	533	9	b	b	X
ejpam-6178	533	10	’	'	PUNCT
ejpam-6178	533	11	,	,	PUNCT
ejpam-6178	533	12	’	'	PUNCT
ejpam-6178	533	13	c	c	X
ejpam-6178	533	14	’	'	PUNCT
ejpam-6178	533	15	,	,	PUNCT
ejpam-6178	533	16	’	'	PUNCT
ejpam-6178	533	17	d	d	X
ejpam-6178	533	18	’	'	PUNCT
ejpam-6178	533	19	]	]	PUNCT
ejpam-6178	533	20	,	,	PUNCT
ejpam-6178	533	21	[	[	PUNCT
ejpam-6178	533	22	’	'	PUNCT
ejpam-6178	533	23	b	b	X
ejpam-6178	533	24	’	'	PUNCT
ejpam-6178	533	25	,	,	PUNCT
ejpam-6178	533	26	’	'	PUNCT
ejpam-6178	533	27	a	a	PRON
ejpam-6178	533	28	’	'	PUNCT
ejpam-6178	533	29	,	,	PUNCT
ejpam-6178	533	30	’	'	PUNCT
ejpam-6178	533	31	d	d	X
ejpam-6178	533	32	’	'	PUNCT
ejpam-6178	533	33	,	,	PUNCT
ejpam-6178	533	34	’	'	PUNCT
ejpam-6178	533	35	c	c	X
ejpam-6178	533	36	’	'	PUNCT
ejpam-6178	533	37	]	]	PUNCT
ejpam-6178	533	38	,	,	PUNCT
ejpam-6178	533	39	[	[	PUNCT
ejpam-6178	533	40	’	'	PUNCT
ejpam-6178	533	41	c	c	NOUN
ejpam-6178	533	42	’	'	PUNCT
ejpam-6178	533	43	,	,	PUNCT
ejpam-6178	533	44	’	'	PUNCT
ejpam-6178	533	45	d	d	X
ejpam-6178	533	46	’	'	PUNCT
ejpam-6178	533	47	,	,	PUNCT
ejpam-6178	533	48	’	'	PUNCT
ejpam-6178	533	49	a	a	DET
ejpam-6178	533	50	’	'	PUNCT
ejpam-6178	533	51	,	,	PUNCT
ejpam-6178	533	52	’	'	PUNCT
ejpam-6178	533	53	b	b	X
ejpam-6178	533	54	’	'	PUNCT
ejpam-6178	533	55	]	]	PUNCT
ejpam-6178	533	56	,	,	PUNCT
ejpam-6178	533	57	[	[	PUNCT
ejpam-6178	533	58	’	'	PUNCT
ejpam-6178	533	59	d	d	NOUN
ejpam-6178	533	60	’	'	PUNCT
ejpam-6178	533	61	,	,	PUNCT
ejpam-6178	533	62	’	'	PUNCT
ejpam-6178	533	63	c	c	X
ejpam-6178	533	64	’	'	PUNCT
ejpam-6178	533	65	,	,	PUNCT
ejpam-6178	533	66	’	'	PUNCT
ejpam-6178	533	67	b	b	X
ejpam-6178	533	68	’	'	PUNCT
ejpam-6178	533	69	,	,	PUNCT
ejpam-6178	533	70	’	'	PUNCT
ejpam-6178	533	71	a	a	PRON
ejpam-6178	533	72	’	'	PUNCT
ejpam-6178	533	73	]	]	PUNCT
ejpam-6178	533	74	]	]	PUNCT
ejpam-6178	533	75	elements_b	elements_b	X
ejpam-6178	534	1	=	=	PUNCT
ejpam-6178	534	2	[	[	PUNCT
ejpam-6178	534	3	’	'	PUNCT
ejpam-6178	534	4	a	a	PRON
ejpam-6178	534	5	’	'	PUNCT
ejpam-6178	534	6	,	,	PUNCT
ejpam-6178	534	7	’	'	PUNCT
ejpam-6178	534	8	b	b	X
ejpam-6178	534	9	’	'	PUNCT
ejpam-6178	534	10	,	,	PUNCT
ejpam-6178	534	11	’	'	PUNCT
ejpam-6178	534	12	c	c	X
ejpam-6178	534	13	’	'	PUNCT
ejpam-6178	534	14	,	,	PUNCT
ejpam-6178	534	15	’	'	PUNCT
ejpam-6178	534	16	d	d	X
ejpam-6178	534	17	’	'	PUNCT
ejpam-6178	534	18	]	]	PUNCT
ejpam-6178	534	19	cayley_table_b	cayley_table_b	NOUN
ejpam-6178	535	1	=	=	PUNCT
ejpam-6178	535	2	[	[	PUNCT
ejpam-6178	535	3	[	[	PUNCT
ejpam-6178	535	4	’	'	PUNCT
ejpam-6178	535	5	a	a	PRON
ejpam-6178	535	6	’	'	PUNCT
ejpam-6178	535	7	,	,	PUNCT
ejpam-6178	535	8	’	'	PUNCT
ejpam-6178	535	9	b	b	X
ejpam-6178	535	10	’	'	PUNCT
ejpam-6178	535	11	,	,	PUNCT
ejpam-6178	535	12	’	'	PUNCT
ejpam-6178	535	13	c	c	X
ejpam-6178	535	14	’	'	PUNCT
ejpam-6178	535	15	,	,	PUNCT
ejpam-6178	535	16	’	'	PUNCT
ejpam-6178	535	17	d	d	X
ejpam-6178	535	18	’	'	PUNCT
ejpam-6178	535	19	]	]	PUNCT
ejpam-6178	535	20	,	,	PUNCT
ejpam-6178	535	21	[	[	PUNCT
ejpam-6178	535	22	’	'	PUNCT
ejpam-6178	535	23	b	b	X
ejpam-6178	535	24	’	'	PUNCT
ejpam-6178	535	25	,	,	PUNCT
ejpam-6178	535	26	’	'	PUNCT
ejpam-6178	535	27	a	a	PRON
ejpam-6178	535	28	’	'	PUNCT
ejpam-6178	535	29	,	,	PUNCT
ejpam-6178	535	30	’	'	PUNCT
ejpam-6178	535	31	d	d	X
ejpam-6178	535	32	’	'	PUNCT
ejpam-6178	535	33	,	,	PUNCT
ejpam-6178	535	34	’	'	PUNCT
ejpam-6178	535	35	c	c	X
ejpam-6178	535	36	’	'	PUNCT
ejpam-6178	535	37	]	]	PUNCT
ejpam-6178	535	38	,	,	PUNCT
ejpam-6178	535	39	[	[	PUNCT
ejpam-6178	535	40	’	'	PUNCT
ejpam-6178	535	41	c	c	NOUN
ejpam-6178	535	42	’	'	PUNCT
ejpam-6178	535	43	,	,	PUNCT
ejpam-6178	535	44	’	'	PUNCT
ejpam-6178	535	45	d	d	X
ejpam-6178	535	46	’	'	PUNCT
ejpam-6178	535	47	,	,	PUNCT
ejpam-6178	535	48	’	'	PUNCT
ejpam-6178	535	49	a	a	DET
ejpam-6178	535	50	’	'	PUNCT
ejpam-6178	535	51	,	,	PUNCT
ejpam-6178	535	52	’	'	PUNCT
ejpam-6178	535	53	b	b	X
ejpam-6178	535	54	’	'	PUNCT
ejpam-6178	535	55	]	]	PUNCT
ejpam-6178	535	56	,	,	PUNCT
ejpam-6178	535	57	[	[	PUNCT
ejpam-6178	535	58	’	'	PUNCT
ejpam-6178	535	59	d	d	NOUN
ejpam-6178	535	60	’	'	PUNCT
ejpam-6178	535	61	,	,	PUNCT
ejpam-6178	535	62	’	'	PUNCT
ejpam-6178	535	63	c	c	X
ejpam-6178	535	64	’	'	PUNCT
ejpam-6178	535	65	,	,	PUNCT
ejpam-6178	535	66	’	'	PUNCT
ejpam-6178	535	67	b	b	X
ejpam-6178	535	68	’	'	PUNCT
ejpam-6178	535	69	,	,	PUNCT
ejpam-6178	535	70	’	'	PUNCT
ejpam-6178	535	71	a	a	PRON
ejpam-6178	535	72	’	'	PUNCT
ejpam-6178	535	73	]	]	PUNCT
ejpam-6178	535	74	]	]	PUNCT
ejpam-6178	535	75	a	a	DET
ejpam-6178	535	76	=	=	X
ejpam-6178	535	77	algebra	algebra	PROPN
ejpam-6178	535	78	(	(	PUNCT
ejpam-6178	535	79	elements_a	elements_a	NOUN
ejpam-6178	535	80	,	,	PUNCT
ejpam-6178	535	81	cayley_table_a	cayley_table_a	PROPN
ejpam-6178	535	82	)	)	PUNCT
ejpam-6178	536	1	b	b	X
ejpam-6178	537	1	=	=	PUNCT
ejpam-6178	538	1	algebra	algebra	PROPN
ejpam-6178	538	2	(	(	PUNCT
ejpam-6178	538	3	elements_b	elements_b	X
ejpam-6178	538	4	,	,	PUNCT
ejpam-6178	538	5	cayley_table_b	cayley_table_b	PROPN
ejpam-6178	538	6	)	)	PUNCT
ejpam-6178	538	7	def	def	PROPN
ejpam-6178	538	8	h	h	NOUN
ejpam-6178	538	9	(	(	PUNCT
ejpam-6178	538	10	element	element	NOUN
ejpam-6178	538	11	)	)	PUNCT
ejpam-6178	538	12	:	:	PUNCT
ejpam-6178	539	1	mapping	mapping	NOUN
ejpam-6178	539	2	=	=	PUNCT
ejpam-6178	539	3	{	{	PUNCT
ejpam-6178	539	4	’	'	PUNCT
ejpam-6178	539	5	a	a	X
ejpam-6178	539	6	’	'	PUNCT
ejpam-6178	539	7	:	:	PUNCT
ejpam-6178	539	8	’	'	PUNCT
ejpam-6178	539	9	a	a	PRON
ejpam-6178	539	10	’	'	PUNCT
ejpam-6178	539	11	,	,	PUNCT
ejpam-6178	539	12	’	'	PUNCT
ejpam-6178	539	13	b	b	X
ejpam-6178	539	14	’	'	PUNCT
ejpam-6178	539	15	:	:	PUNCT
ejpam-6178	539	16	’	'	PUNCT
ejpam-6178	539	17	b	b	X
ejpam-6178	539	18	’	'	PUNCT
ejpam-6178	539	19	,	,	PUNCT
ejpam-6178	539	20	’	'	PUNCT
ejpam-6178	539	21	c	c	X
ejpam-6178	539	22	’	'	PUNCT
ejpam-6178	539	23	:	:	PUNCT
ejpam-6178	539	24	’	'	PUNCT
ejpam-6178	539	25	d	d	X
ejpam-6178	539	26	’	'	PUNCT
ejpam-6178	539	27	,	,	PUNCT
ejpam-6178	539	28	’	'	PUNCT
ejpam-6178	539	29	d	d	X
ejpam-6178	539	30	’	'	PUNCT
ejpam-6178	539	31	:	:	PUNCT
ejpam-6178	539	32	’	'	PUNCT
ejpam-6178	539	33	c	c	X
ejpam-6178	539	34	’	'	PUNCT
ejpam-6178	539	35	}	}	PUNCT
ejpam-6178	539	36	return	return	VERB
ejpam-6178	539	37	mapping	mapping	NOUN
ejpam-6178	539	38	[	[	PUNCT
ejpam-6178	539	39	element	element	NOUN
ejpam-6178	539	40	]	]	PUNCT
ejpam-6178	539	41	r.	r.	PROPN
ejpam-6178	539	42	nuñez	nuñez	PROPN
ejpam-6178	539	43	,	,	PUNCT
ejpam-6178	539	44	k.	k.	PROPN
ejpam-6178	539	45	b.	b.	PROPN
ejpam-6178	539	46	fuentes	fuentes	PROPN
ejpam-6178	539	47	/	/	SYM
ejpam-6178	539	48	eur	eur	PROPN
ejpam-6178	539	49	.	.	PUNCT
ejpam-6178	540	1	j.	j.	PROPN
ejpam-6178	540	2	pure	pure	PROPN
ejpam-6178	540	3	appl	appl	PROPN
ejpam-6178	540	4	.	.	PROPN
ejpam-6178	540	5	math	math	PROPN
ejpam-6178	540	6	,	,	PUNCT
ejpam-6178	540	7	18	18	NUM
ejpam-6178	540	8	(	(	PUNCT
ejpam-6178	540	9	4	4	NUM
ejpam-6178	540	10	)	)	PUNCT
ejpam-6178	540	11	(	(	PUNCT
ejpam-6178	540	12	2025	2025	NUM
ejpam-6178	540	13	)	)	PUNCT
ejpam-6178	540	14	,	,	PUNCT
ejpam-6178	540	15	6178	6178	NUM
ejpam-6178	540	16	15	15	NUM
ejpam-6178	540	17	of	of	ADP
ejpam-6178	540	18	15	15	NUM
ejpam-6178	540	19	i	i	PROPN
ejpam-6178	540	20	f	f	PROPN
ejpam-6178	540	21	is_homomorphism	is_homomorphism	PROPN
ejpam-6178	540	22	(	(	PUNCT
ejpam-6178	540	23	h	h	NOUN
ejpam-6178	540	24	,	,	PUNCT
ejpam-6178	540	25	a	a	DET
ejpam-6178	540	26	,	,	PUNCT
ejpam-6178	540	27	b	b	NOUN
ejpam-6178	540	28	)	)	PUNCT
ejpam-6178	540	29	:	:	PUNCT
ejpam-6178	540	30	print	print	NOUN
ejpam-6178	540	31	(	(	PUNCT
ejpam-6178	540	32	”	"	PUNCT
ejpam-6178	540	33	h	h	PROPN
ejpam-6178	540	34	␣	␣	NOUN
ejpam-6178	541	1	i	i	PRON
ejpam-6178	541	2	s	s	PROPN
ejpam-6178	541	3	␣	␣	PROPN
ejpam-6178	541	4	a	a	DET
ejpam-6178	541	5	␣	␣	ADJ
ejpam-6178	541	6	homomorphism	homomorphism	NOUN
ejpam-6178	541	7	␣	␣	NUM
ejpam-6178	541	8	from	from	ADP
ejpam-6178	541	9	␣	␣	PROPN
ejpam-6178	541	10	a	a	DET
ejpam-6178	541	11	␣	␣	ADJ
ejpam-6178	541	12	to	to	ADP
ejpam-6178	541	13	␣	␣	PROPN
ejpam-6178	541	14	b.	b.	PROPN
ejpam-6178	541	15	”	"	PUNCT
ejpam-6178	541	16	)	)	PUNCT
ejpam-6178	541	17	else	else	ADV
ejpam-6178	541	18	:	:	PUNCT
ejpam-6178	541	19	print	print	NOUN
ejpam-6178	541	20	(	(	PUNCT
ejpam-6178	541	21	”	"	PUNCT
ejpam-6178	541	22	h	h	PROPN
ejpam-6178	541	23	␣	␣	NOUN
ejpam-6178	542	1	i	i	PRON
ejpam-6178	542	2	s	s	PROPN
ejpam-6178	542	3	␣	␣	ADJ
ejpam-6178	542	4	not	not	PART
ejpam-6178	542	5	␣	␣	NOUN
ejpam-6178	542	6	a	a	DET
ejpam-6178	542	7	␣	␣	ADJ
ejpam-6178	542	8	homomorphism	homomorphism	NOUN
ejpam-6178	542	9	␣	␣	NUM
ejpam-6178	542	10	from	from	ADP
ejpam-6178	542	11	␣	␣	PROPN
ejpam-6178	542	12	a	a	PRON
ejpam-6178	542	13	␣	␣	ADJ
ejpam-6178	542	14	to	to	ADP
ejpam-6178	542	15	␣	␣	PROPN
ejpam-6178	542	16	b.	b.	PROPN
ejpam-6178	542	17	”	"	PUNCT
ejpam-6178	542	18	)	)	PUNCT
ejpam-6178	542	19	output	output	NOUN
ejpam-6178	542	20	:	:	PUNCT
ejpam-6178	542	21	ps	ps	NOUN
ejpam-6178	542	22	c	c	NOUN
ejpam-6178	542	23	:	:	PUNCT
ejpam-6178	542	24	\	\	NUM
ejpam-6178	542	25	users	user	NOUN
ejpam-6178	542	26	\	\	PROPN
ejpam-6178	542	27	johar	johar	PROPN
ejpam-6178	542	28	>	>	X
ejpam-6178	542	29	&	&	CCONJ
ejpam-6178	542	30	c:/	c:/	PROPN
ejpam-6178	542	31	users	user	NOUN
ejpam-6178	542	32	/	/	SYM
ejpam-6178	542	33	johar	johar	PROPN
ejpam-6178	542	34	/onedrive	/onedrive	PROPN
ejpam-6178	542	35	/	/	SYM
ejpam-6178	542	36	documents	document	NOUN
ejpam-6178	542	37	/	/	SYM
ejpam-6178	542	38	phyton	phyton	PROPN
ejpam-6178	542	39	/	/	SYM
ejpam-6178	542	40	python	python	PROPN
ejpam-6178	542	41	.	.	PUNCT
ejpam-6178	543	1	exe	exe	NOUN
ejpam-6178	543	2	”	"	PUNCT
ejpam-6178	544	1	c	c	NOUN
ejpam-6178	544	2	:	:	PUNCT
ejpam-6178	544	3	/	/	SYM
ejpam-6178	544	4	users	user	NOUN
ejpam-6178	544	5	/	/	SYM
ejpam-6178	544	6	johar	johar	PROPN
ejpam-6178	544	7	/onedrive	/onedrive	PROPN
ejpam-6178	544	8	/	/	SYM
ejpam-6178	544	9	documents	document	NOUN
ejpam-6178	544	10	/	/	SYM
ejpam-6178	544	11	ms_thesis_proposal/	ms_thesis_proposal/	NOUN
ejpam-6178	544	12	proposal	proposal	NOUN
ejpam-6178	544	13	␣	␣	ADJ
ejpam-6178	545	1	−	−	NUM
ejpam-6178	545	2	␣	␣	ADJ
ejpam-6178	545	3	copy	copy	NOUN
ejpam-6178	545	4	/	/	SYM
ejpam-6178	545	5	test	test	NOUN
ejpam-6178	545	6	␣	␣	ADJ
ejpam-6178	545	7	folder	folder	NOUN
ejpam-6178	545	8	/homomorphism	/homomorphism	NOUN
ejpam-6178	545	9	.	.	PUNCT
ejpam-6178	546	1	py	py	PROPN
ejpam-6178	546	2	”	"	PUNCT
ejpam-6178	546	3	h	h	NOUN
ejpam-6178	547	1	i	i	PRON
ejpam-6178	547	2	s	s	VERB
ejpam-6178	547	3	a	a	DET
ejpam-6178	547	4	homomorphism	homomorphism	NOUN
ejpam-6178	547	5	from	from	ADP
ejpam-6178	547	6	a	a	PRON
ejpam-6178	547	7	to	to	ADP
ejpam-6178	547	8	b.	b.	PROPN
ejpam-6178	547	9	ps	ps	PROPN
ejpam-6178	547	10	c	c	PROPN
ejpam-6178	547	11	:	:	PUNCT
ejpam-6178	547	12	\	\	NUM
ejpam-6178	547	13	users	user	NOUN
ejpam-6178	547	14	\	\	PROPN
ejpam-6178	547	15	johar	johar	PROPN
ejpam-6178	547	16	>	>	X